Anytime heuristic search algorithms try to find a (potentially suboptimal) solution as quickly as possible and then work to find better and better solutions until an optimal solution is obtained or time is exhausted. The most widely-known anytime search algorithms are based on best-first search. In this paper, we propose a new algorithm, rectangle search, that is instead based on beam search, a variant of breadth-first search. It repeatedly explores alternatives at all depth levels and is thus best-suited to problems featuring deep local minima. Experiments using a variety of popular search benchmarks suggest that rectangle search is competitive with fixed-width beam search and often performs better than the previous best anytime search algorithms.

This paper studies the equivalence problem for relational pattern languages, where a relation imposes dependencies between the two strings with which two variables in a pattern can be replaced simultaneously. Our focus is on the question whether the non-equivalence of two relational patterns is witnessed by short strings, namely those generated by replacing variables in the patterns by strings of length bounded by some (small) number $z$. After establishing a close connection between this problem and the study of the notions of \emph{teaching dimension}\/{and} \emph{no-clash teaching dimension}, we investigate specific classes of relational pattern languages. We show that the smallest number $z$ that serves as a bound for testing equivalence is $2$ when the relation between variable substitutions is that of equal string length, and the alphabet size it at least 3. This has interesting implications on the size and form of non-clashing teaching sets for the corresponding languages. By contrast, not even $z=3$ is sufficient when the constraints require two substituted strings to be the reversal of one another, for alphabets of size 2. We conclude with a negative result on erasing pattern languages.

To assess the trustworthiness of an agent in a multi-agent system, one often combines two types of trust information: direct trust information derived from one's own interactions with that agent, and indirect trust information based on advice from other agents. This paper provides the first systematic study on when it is beneficial to combine these two types of trust as opposed to relying on only one of them. Our large-scale experimental study shows that strong methods for computing indirect trust make direct trust redundant in a surprisingly wide variety of scenarios. Further, a new method for the combination of the two trust types is proposed that, in the remaining scenarios, outperforms the ones known from the literature.

Edelkamp et al. (2005) proved that A*, given an admissible heuristic, is guaranteed to return an optimal solution in any cost algebra, not just in the traditional shortest path setting. In this paper, we investigate cost-algebraic A*’s optimal efficiency: in the cost-algebraic setting, under what conditions is A* guaranteed to expand the fewest possible states? In the traditional setting, this question was examined in detail by Dechter & Pearl (1985). They identified five different situations in which A* was optimally efficient. We show that three of them continue to hold in the cost-algebraic setting, but that one does not. We also show that one of them is false, it does not hold even in the traditional setting. We introduce an alternative that does hold in the cost-algebraic setting. Finally, we show that a well-known result due to Nilsson does not hold in the general cost-algebraic setting but does hold in a slightly less general setting.

Weighted A* (wA*) is a widely used algorithm for rapidly, but suboptimally, solving planning and search problems. The cost of the solution it produces is guaranteed to be at most W times the optimal solution cost, where W is the weight wA* uses in prioritizing open nodes. W is therefore a suboptimality bound for the solution produced by wA*. There is broad consensus that this bound is not very accurate, that the actual suboptimality of wA*'s solution is often much less than W times optimal. However, there is very little published evidence supporting that view, and no existing explanation of why W is a poor bound. This paper fills in these gaps in the literature. We begin with a large-scale experiment demonstrating that, across a wide variety of domains and heuristics for those domains, W is indeed very often far from the true suboptimality of wA*'s solution. We then analytically identify the potential sources of error. Finally, we present a practical method for correcting for two of these sources of error and experimentally show that the corrections frequently eliminate much of the error.

It is well-known that any admissible unidirectional heuristic search algorithm must expand all states whose f-value is smaller than the optimal solution cost when using a consistent heuristic. Such states are called “surely expanded” (s.e.). A recent study characterized s.e. pairs of states for bidirectional search with consistent heuristics: if a pair of states is s.e. then at least one of the two states must be expanded. This paper derives a lower bound, VC, on the minimum number of expansions required to cover all s.e. pairs, and present a new admissible front-to-end bidirectional heuristic search algorithm, Near-Optimal Bidirectional Search (NBS), that is guaranteed to do no more than 2VC expansions. We further prove that no admissible front-to-end algorithm has a worst case better than 2VC. Experimental results show that NBS competes with or outperforms existing bidirectional search algorithms, and often outperforms A* as well.

In many planning applications, actions can have highly diverse costs. Recent studies focus on the effects of diverse action costs on search algorithms, but not on their effects on domain-independent heuristics. In this paper, we demonstrate there are negative impacts of action cost diversity on merge-and-shrink (M&S), a successful abstraction method for producing high-quality heuristics for planning problems. We propose a new cost partitioning method for M&S to address the negative effects of diverse action costs. We investigate non-unit cost IPC domains, especially those for which diverse action costs have severe negative effects on the quality of the M&S heuristic. Our experiments demonstrate that in these domains, an additive set of M&S heuristics using the new cost partitioning method produces much more informative and effective heuristics than creating a single M&S heuristic which directly encodes diverse costs.

We present MM, the first bidirectional heuristic search algorithm whose forward and backward searches are guaranteed to ''meet in the middle'', i.e. never expand a node beyond the solution midpoint. We also present a novel framework for comparing MM, A*, and brute-force search, and identify conditions favoring each algorithm. Finally, we present experimental results that support our theoretical analysis.

Bidirectional search algorithms interleave a search forward from the start state (start ) and a search backward (i.e. using reverse operators) from the goal state (goal). We say that the two searches “meet in the middle” if neither search expands a node whose g-value (in the given direction) exceeds C*/2 , where C* is the cost of an optimal solution. The only bidirectional heuristic search algorithm that is guaranteed to meet in the middle under all circumstances is the recently introduced MM algorithm (Holte et al. 2016). The feature of MM that provides this guarantee is its unique priority functions for nodes on its open lists. In this short note we present MMe, which enhances MM’s priority function and is expected to expand fewer nodes than MM under most circumstances. We sketch a proof of MMe’s correctness, describe conditions under which MMe will expand fewer nodes than MM and vice versa, and experimentally compare MMe and MM on the 10-Pancake problem.

Pruning techniques have recently been shown to speed up search algorithms by reducing the branching factor of large search spaces. One such technique is sleep sets, which were originally introduced as a pruning technique for model checking, and which have recently been investigated on a theoretical level for planning. In this paper, we propose a generalization of sleep sets and prove its correctness. While the original sleep sets were based on the commutativity of operators, generalized sleep sets are based on a more general notion of operator sequence redundancy. As a result, our approach dominates the original sleep sets variant in terms of pruning power. On a practical level, our experimental evaluation shows the potential of sleep sets and their generalizations on a large and common set of planning benchmarks.

Abstraction is a powerful technique in search and planning. A fundamental problem of abstraction is that it can create spurious paths, i.e., abstract paths that do not correspond to valid concrete paths. In this paper, we define spurious paths as a generalization of spurious states. We show that spurious paths can be categorized into two types: state-independent spurious paths and state-specific spurious paths. We present a practical method that eliminates state-independent spurious paths, as well as state-specific spurious paths when integrated with mutex detection methods. We provide syntactical conditions under which our method can remove state-independent spurious paths completely. We demonstrate that eliminating spurious paths can improve a heuristic substantially, even in abstract spaces that are free of spurious states.

Greedy Best-First Search (GBFS) is a powerful algorithm at the heart of many state of the art satisficing planners. One major weakness of GBFS is its behavior in so-called uninformative heuristic regions (UHRs) - parts of the search space in which no heuristic provides guidance towards states with improved heuristic values. This work analyzes the problem of UHRs in planning in detail, and proposes a two level search framework as a solution. In Greedy Best-First Search with Local Exploration (GBFS-LE), a local exploration is started from within a global GBFS whenever the search seems stuck in UHRs. Two different local exploration strategies are developed and evaluated experimentally: Local GBFS (LS) and Local Random Walk Search (LRW). The two new planners LAMA-LS and LAMA-LRW integrate these strategies into the GBFS component of LAMA-2011. Both are shown to yield clear improvements in terms of both coverage and search time on standard International Planning Competition benchmarks, especially for domains that are proven to have large or un- bounded UHRs.

Utilizing multiple queues in Greedy Best-First Search (GBFS) has been proven to be a very effective approach to satisficing planning. Successful techniques include extra queues based on Helpful Actions (or Preferred Operators), as well as using Multiple Heuristics. One weakness of all standard GBFS algorithms is their lack of exploration. All queues used in these methods work as priority queues sorted by heuristic values. Therefore, misleading heuristics, especially early in the search process, can cause the search to become ineffective. Type systems, as introduced for heuristic search by Lelis et al, are a development of ideas for exploration related to the classic stratified sampling approach. The current work introduces a search algorithm that utilizes type systems in a new way – for exploration within a GBFS multiqueue framework in satisficing planning. A careful case study shows the benefits of such exploration for overcoming deficiencies of the heuristic. The proposed new baseline algorithm Type-GBFS solves almost 200 more problems than baseline GBFS over all International Planning Competition problems. Type-LAMA, a new planner which integrates Type-GBFS into LAMA-2011, solves 36.8 more problems than LAMA-2011.

A* with lookahead (AL*) is a variant of A* that performs a cost-bounded DFS lookahead from a node when it is generated. We show that the original version of AL* (AL*0) can, in some circumstances, fail to return an optimal solution because of the move pruning it does. We present two new versions, AL*1 and ELH, that we prove to always be correct and give conditions in which AL*0 is guaranteed to be correct. In our experiments with unit costs, AL*0 was usually the fastest AL* version, but its advantage was usually small. In our experiments with non-unit costs, AL*0 substantially outperforms both A* and IDA*. We also evaluate the idea of immediately expanding a generated node if it has the same f-value as its parent. We find that doing so causes AL* to require more memory and sometimes slows AL* down.

Merge-and-shrink is a general method for deriving accurate abstraction heuristics.We present two novel nonlinear merging strategies, UMC and MIASM, based on variable interaction. The principle underlying our methods is to merge strongly interacting variables early on. UMC measures variable interaction by weighted causal graph edges, and MIASM measures variable interaction in terms of the number of necessary states in the abstract space defined by the variables. The methods partition variables into clusters in which the variable interactions are strong, and merge variables within each cluster before merging the clusters. Experiment results show that our merging strategies outperform existing merging strategies in general and can produce heuristics that give perfect guidance for solving tasks that previous methods cannot even solve.

When solving instances of problem domains that feature a large branching factor, A* may generate a large number of nodes whose cost is greater than the cost of the optimal solution. We designate such nodes as surplus. Generating surplus nodes and adding them to the OPEN list may dominate both time and memory of the search. A recently introduced variant of A* called Partial Expansion A* (PEA*) deals with the memory aspect of this problem. When expanding a node n, PEA* generates all of its children and puts into OPEN only the children with f = f (n). n is re-inserted in the OPEN list with the f -cost of the best discarded child. This guarantees that surplus nodes are not inserted into OPEN. In this paper, we present a novel variant of A* called Enhanced Partial Expansion A* (EPEA*) that advances the idea of PEA* to address the time aspect. Given a priori domain- and heuristic- specific knowledge, EPEA* generates only the nodes with f = f(n). Although EPEA* is not always applicable or practical, we study several variants of EPEA*, which make it applicable to a large number of domains and heuristics. In particular, the ideas of EPEA* are applicable to IDA* and to the domains where pattern databases are traditionally used. Experimental studies show significant improvements in run-time and memory performance for several standard benchmark applications. We provide several theoretical studies to facilitate an understanding of the new algorithm.

It is known that A* is optimal with respect to the expanded nodes (Dechter and Pearl 1985) (D&P). The exact meaning of this optimality varies depending on the class of algorithms and instances over which A* is claimed to be optimal. A* does not provide any optimality guarantees with respect to the generated nodes. However, such guarantees may be critical for optimally solving instances of domains with a large branching factor. In this paper, we introduce two new variants of the recently introduced Enhanced Partial Expansion A* algorithm (EPEA*) (Felner et al. 2012). We leverage the results of D&P to show that these variants possess optimality with respect to the generated nodes in much the same sense as A* possesses optimality with respect to the expanded nodes. The results in this paper are theoretical. A study of the practical performance of the new variants is beyond the scope of this paper.

A* is often described as being `optimal', in that it expands the minimum number of unique nodes. But, A* may generate many extra nodes which are never expanded. This is a performance loss, especially when the branching factor is large. Partial Expansion A* addresses this problem when expanding a node, n, by generating all the children of n but only storing children with the same f-cost as n. n is re-inserted into the OPEN list, but with the f-cost of the next best child. This paper introduces an enhanced version of PEA* (EPEA*). Given a priori domain knowledge, EPEA* generates only the children with the same f-cost as the parent. EPEA* is generalized to its iterative-deepening variant, EPE-IDA*. For some domains, these algorithms yield substantial performance improvements. State-of-the-art results were obtained for the pancake puzzle and for some multi-agent pathfinding instances. Drawbacks of EPEA* are also discussed.

In extensive-form games with a large number of actions, careful abstraction of the action space is critically important to performance. In this paper we extend previous work on action abstraction using no-limit poker games as our test domains. We show that in such games it is no longer necessary to choose, a priori, one specific range of possible bet sizes. We introduce an algorithm that adjusts the range of bet sizes considered for each bet individually in an iterative fashion. This flexibility results in a substantially improved game value in no-limit Leduc poker. When applied to no-limit Texas Hold'em our algorithm produces an action abstraction that is about one third the size of a state of the art hand-crafted action abstraction, yet has a better overall game value.

Korf, Reid and Edelkamp initiated a line of research for developing methods (KRE and later CDP) that predict the number of nodes expanded by IDA* for a given start state and cost bound. Independent of that, Chen developed a method (SS) that can also be used to predict the number of nodes expanded by IDA*. In this paper we advance both of these prediction methods. First, we develop a variant of CDP that can be orders of magnitude faster than CDP while producing exactly the same predictions. Second, we show how ideas developed in the KRE line of research can be used to substantially improve the predictions produced by SS. Third, we make an empirical comparison between our new enhanced versions of CDP and SS. Our experimental results point out that CDP is suitable for applications that require less accurate but very fast predictions, while SS is suitable for applications that require more accurate predictions but allow more computation time.

In this paper we show that the move pruning method we presented at SoCS last year sometimes prunes all the least-cost paths from one state to another. We present two examples exhibiting this erroneous behaviour--a simple, artificial example and a slightly more complex example that arose in last year's experiments. We then formally prove that a simple modification to our move pruning method makes it "safe," i.e., it will never prune all the least-cost paths between a pair of states. Finally, we present the results of rerunning last year's experiments with this provably safe version of move pruning and show that last year's main conclusions still hold, namely: (1) in domains where there are short redundant sequences move pruning produces substantial speedups in depth-first search, and (2) in domains where the only short redundant sequences are 2-cycles, move pruning is faster than parent pruning by a factor of two or more.

A* is often described as being 'optimal,' in that it expands the minimum number of unique nodes. But, A* may generate many extra nodes which are never expanded. This is a performance loss, especially when the branching factor is large. Partial Expansion A* (PEA*) addresses this problem when expanding a node, n, by generating all the children of n but only storing children with the same f-cost as n. We introduce an enhanced version of PEA* (EPEA*). Given a priori domain knowledge, EPEA* only generates the children with the same f-cost as the parent. State-of-the-art results were obtained for a number of domains. Drawbacks of EPEA* are also discussed. A full version of this paper appears in the proceedings of AAAI-2012

Jabbari Arfaee, Zilles, and Holte presented the bootstrap learning system, a system that learns strong heuristic functions for state-space problems. They showed that IDA* with a bootstrap heuristic is able to quickly find near-optimal solutions in several problem domains. However, the process the bootstrap method uses to learn heuristic functions is time-consuming: it is on the order of days. In this paper we present a learning system that uses an approximation method instead of an exact one to generate the training set required to learn heuristics. We showed recently that solution costs can often be quickly and accurately predicted without having to actually find a solution. In this paper we apply this idea to speedup the process of learning heuristics. In contrast with other learning approaches that use search algorithms to solve problem instances to generate the training set, our system uses a solution cost predictor. We reduce the time required to learn strong heuristics from days to minutes on the domains tested.

Optimal planning and heuristic search systems solve state-space searchproblems by finding a least-cost path from start to goal. As a byproduct of having an optimal path they also determine the optimal solution cost. In this paper we focus on the problem of determining the optimal solution cost for a state-space search problem directly, i.e., without actually finding a solution path of that cost. We present an efficient algorithm, BiSS, based on ideas of bidirectional search and stratified sampling that produces accurate estimates of the optimal solution cost. Our method is guaranteed to return the optimal solution cost in the limit as the sample size goes to infinity.

In this paper we introduce a broadly applicable method, called multimapping abstraction, that allows multiple heuristic values for a state to be extracted from one abstract state space. The key idea is to define an abstraction to be a multimapping, i.e., a function that maps a state in the original state space to a set of states in the abstract space. We performed a large-scale experiment on several benchmark state spaces to compare the memory requirements and runtime of Hierarchical IDA* (HIDA*) using multimapping domain abstractions to HIDA* with individual domain abstractions and to HIDA* with multiple, independent domain abstractions. Our results show that multimapping domain abstractions are superior to both alternatives in terms of both memory usage and runtime.

The notion of finding a solution that is approximately optimal with high probability was recently introduced to the field of heuristic search,formalized as Probably Approximately Correct Heuristic Search, or PAC search in short. A big challenge when constructing a PAC search algorithm is to identify when a given solution achieves the desired sub-optimality with the required confidence, allowing the search to halt and return the incumbent solution. In this paper we propose two novel methods for identifying when a PAC search can halt. Unlike previous work, the new methods provided in this paper become more knowledgeable as the search progresses. This can speedup the search, since the search can halt earlier with the proposed methods and still keeping the desired PAC solution quality guarantees.Experimental results indeed show a substantial speedup of the search in comparison to the previous approach for PAC search.

Multi-agent decision problems can often be formulated as extensive-form games. We focus on imperfect information extensive-form games in which one or more actions at many decision points have an associated continuous or many-valued parameter. A stock trading agent, in addition to deciding whether to buy or not, must decide how much to buy. In no-limit poker, in addition to selecting a probability for each action, the agent must decide how much to bet for each betting action. Selecting values for these parameters makes these games extremely large. Two-player no-limit Texas Hold'em poker with stacks of 500 big blinds has approximately 1071 states, which is more than 1050 times more states than two-player limit Texas Hold'em. The main contribution of this paper is a technique that abstracts a game's action space by selecting one, or a small number, of the many values for each parameter. We show that strategies computed using this new algorithm for no-limit Leduc poker exhibit significant utility gains over epsilon-Nash equilibrium strategies computed with standard, hand-crafted parameter value abstractions.

Korf, Reid, and Edelkamp launched a line of research aimed at predicting how many nodes IDA* will expand with a given depth bound. This paper advances this line of research in three ways. First, we identify a source of prediction error that has hitherto been overlooked. We call it the "discretization effect." Second, we disprove the intuitively appealing idea that a "more informed" prediction system cannot make worse predictions than a ``less informed'' one. More informed systems are more susceptible to the discretization effect, and in our experiments the more informed system makes poorer predictions. Our third contribution is a method, called "Epsilon-truncation," which makes a prediction system less informed, in a carefully chosen way, so as to improve its predictions by reducing the discretization effect. In our experiments Epsilon-truncation improved predictions substantially.

We present three new ideas for grid-based path-planning algorithms that improve the search speed and quality of the paths found. First, we introduce a new type of database, the Local Distance Database (LDDB), that contains distances between boundary points of a local neighborhood. Second, an LDDB based algorithm is introduced, called Block A*, that calculates the optimal path between start and goal locations given the local distances stored in the LDDB. Third, our experimental results for any-angle path planning in a wide variety of test domains, including real game maps, show that Block A* is faster than both A* and the previously best grid-based any-angle search algorithm, Theta*.

Move pruning is a low-overhead technique for reducing the size of a depth first search tree. The existing algorithm for automatically discovering move pruning information is restricted to games where all moves can be applied to every state. This paper demonstrates an algorithm which handles a general class of single player games. It gives experimental results for our technique, demonstrating both the applicability to a range of games, and the reduction in search tree size. We also provide some conditions under which move pruning is safe, and when it may interfere with other search reduction techniques.

Multi-agent pathfinding, where multiple agents must travel to their goal locations without getting stuck, has been studied in both theoretical and practical contexts, with a variety of both optimal and sub-optimal algorithms proposed for solving problems. Recent work has shown that there is a linear-time check for whether a multi-agent pathfinding problem can be solved in a tree, however this was not used to actually produce solutions. In this paper we provide a constructive proof of how to solve multi-agent pathfinding problems in a tree that culminates in a novel approach that we call the tree-based agent swapping strategy (TASS). Experimental results showed that TASS can find solutions to the multi-agent pathfinding problem on a highly crowded tree with 1000 nodes and 996 agents in less than 8 seconds. These results are far more efficient and general than existing work, suggesting that TASS is a productive line of study for multi-agent pathfinding.

In problem domains for which an informed admissible heuristic function is not available, one attractive approach is hierarchical search. Hierarchical search uses search in an abstracted version of the problem to dynamically generate heuristic values. This paper makes two contributions to hierarchical search. First, we propose a simple modification to the state-of-the-art algorithm Switchback that reduces the number of expansions (and hence the running time) by approximately half, while maintaining its guarantee of optimality. Second, we propose a new algorithm for suboptimal hierarchical search, called Switch. Empirical results suggest that Switch yields faster search than straightforward modifications of Switchback, such as weighting the heuristic or greedy search. The success of Switch illustrates the potential for further research on specifically suboptimal hierarchical search.

Korf, Reid, and Edelkamp launched a line of research aimed at predicting how many nodes IDA* will expand with a given cost bound. This paper advances this line of research in three ways. First, we identify a source of prediction error that has hitherto been overlooked. We call it the ``discretization effect''. Second, we disprove the intuitively appealing idea that a ``more informed'' prediction system cannot make worse predictions than a ``less informed'' one. More informed systems are more susceptible to the discretization effect, and in several of our experiments the more informed system makes poorer predictions. Our third contribution is a method, called ``$\epsilon$-truncation'', which makes a prediction system less informed, in a carefully chosen way, so as to improve its predictions by reducing the discretization effect. In our experiments $\epsilon$-truncation rarely degraded predictions; in the vast majority of cases it improved predictions, often substantially.

State-set search is state space search when the states being manipulated by the search algorithm are sets of states from some underlying state space. State-set search arises commonly in planning and abstraction systems, but this paper provides the first formal, general analysis of state-set search. We show that the state-set distance computed by planning systems is different than that computed by abstraction systems and introduce a distance in between the two, dww, the maximum admissible distance. We introduce the concept of a multi-abstraction, which maps a state to more than one abstract state in the same abstract space, describe the first implementation of a multi-abstraction system that computes dww, and give initial experimental evidence that it can be superior to domain abstraction.

A* is a best-first search algorithm that returns an optimal solution. w-admissible algorithms guarantee that the returned solution is no larger than w times the optimal solution. In this paper we introduce a generalization of the w-admissibility concept that we call PAC search, which is inspired by the PAC learning framework in Machine Learning. The task of a PAC search algorithm is to find a solution that is w-admissible with high probability. In this paper we formally define PAC search, and present a framework for PAC search algorithms that can work on top of any search algorithm that produces a sequence of solutions. Experimental results on the 15-puzzle demonstrate that our framework activated on top of Anytime Weighted A* (AWA*) expands significantly less nodes than regular AWA* while returning solutions that have almost the same quality.

We present three new ideas for grid-based path-planning algorithms that improve the search speed and quality of the paths found. First, we introduce a new type of database, the Local Distance Database (LDDB), that contains distances between boundary points of a local neighborhood. Second, an LDDB-based algorithm is introduced, called Block A*, that calculates the optimal path between start and goal locations given the local distances stored in the LDDB. Third, our experimental results for any-angle path planning in a wide varietyof test domains, including real game maps, show that Block A* is faster than both A* and the previously best grid-based any-angle search algorithm, Theta*.

In problem domains where an informative heuristic evaluation function is not known or not easily computed, abstraction can be used to derive admissible heuristic values. Optimal path lengths in the abstracted problem are consistent heuristic estimates for the original problem. Pattern databases are the traditional method of creating such heuristics, but they exhaustively compute costs for all abstract states and are thus usually appropriate only when all instances share the same single goal state. Hierarchical heuristic search algorithms address these shortcomings by searching for paths in the abstract space on an as-needed basis. However, existing hierarchical algorithms search less efficiently than pattern database constructors: abstract nodes may be expanded many times during the course of a base-level search. We present a novel hierarchical heuristic search algorithm, called Switchback, that uses an alternating direction of search to avoid abstract node re-expansions. This algorithm is simple to implement and demonstrates superior performance to existing hierarchical heuristic search algorithms on several standard benchmarks.

We present an algorithm that exploits the complimentary benefits of best-first search (BFS) and depth-first search (DFS) by performing limited DFS lookaheads from the frontier of BFS. We show that this continuum requires significantly less memory than BFS. In addition, a time speedup is also achieved when choosing the lookahead depth correctly. We demonstrate this idea for breadth-first search and for A*. Additionally, we show that when using inconsistent heuristics, Bidirectional Pathmax (BPMX), can be implemented very easily on top of the lookahead phase. Experimental results on several domains demonstrate the benefits of all our ideas.

An important part of the creation of a housing subdivision is the design and layout of sewers underneath the road. This is a challenging cost optimization problem in a continuous threedimensional space. In this paper, heuristic-search-based techniques are proposed for tackling this problem. The result is new algorithms that can quickly find near optimal solutions that offer important reductions in the cost of design and construction.

search algorithms such as IDA* or heuristic-search planners. Our method aims to generate a strong heuristic from a given weak heuristic h0 through bootstrapping. The "easy" problem instances that can be solved using h0 provide training examples for a learning algorithm that produces a heuristic h1 that is expected to be stronger than h0. If h0 is too weak to solve any of the given instances we use a random walk technique to create a sequence of successively more difficult instances starting with ones that are solvable by h0. The bootstrap process is then repeated using hi in lieu of hi–1 until a sufficiently strong heuristic is produced. We test our method on the 15- and 24-sliding tile puzzles, the 17- and 24-pancake puzzles, and the 15- and 20-blocks world. In every case our method produces a heuristic that allows IDA* to solve randomly generated problem instances extremely quickly with solutions very close to optimal.

This paper examines the following statements about heuristic search, which are commonly held to be true:More accurate heuristics result in fewer node expansions by A* and IDA*.A* does fewer node expansions than any other equally informed algorithm that finds optimal solutions. Any admissible heuristic can be turned into a consistent heuristic by a simple technique called pathmax.In search spaces whose operators all have the same cost A* with the heuristic function h(s)=0 for all states, s, is the same as breadth-first search.Bidirectional A* stops when the forward and backward search frontiers meet.The paper demonstrates that all these statements are false and provides alternative statements that are true.

Korf, Reid, and Edelkamp introduced a formula to predict the number of nodes IDA* will expand on a single iteration for a given consistent heuristic, and experimentally demonstrated that it could make very accurate predictions. In this paper we show that, in addition to requiring the heuristic to be consistent, their formula's predictions are accurate only at levels of the brute-force search tree where the heuristic values obey the unconditional distribution that they defined and then used in their formula. We then propose a new formula that works well without these requirements, i.e., it can make accurate predictions of IDA*'s performance for inconsistent heuristics and if the heuristic values in any level do not obey the unconditional distribution. In order to achieve this we introduce the conditional distribution of heuristic values which is a generalization of their unconditional heuristic distribution. We also provide extensions of our formula that handle individual start states and the augmentation of IDA* with bidirectional pathmax (BPMX), a technique for propagating heuristic values when inconsistent heuristics are used. Experimental results demonstrate the accuracy of our new method and all its variations.

This paper introduces and analyzes a new approach to query suggestion. After the user issues a query q_0, for every document retrieved in a certain rank range [Theta_1,Theta_2], a query search procedure constructs queries that rank the document high enough for the user to see it. From this set of queries the suggestions to be presented to the user are then selected so as to give the best possible access to the documents that were ranked in [Theta_1,Theta_2] for the user's initial query q_0. This approach turns out to be successful under certain assumptions, which are discussed in this paper.

A pattern database (PDB) is a heuristic function implemented as a lookup table. It stores the lengths of optimal solutions for instances of subproblems. Most previous PDBs had a distinct entry in the table for each subproblem instance. In this paper we apply learning techniques to compress PDBs by using neural networks and decision trees thereby reducing the amount of memory needed. Experiments on the sliding tile puzzles and the TopSpin puzzle show that our compressed PDBs significantly outperforms both uncompressed PDBs as well as previous compressing methods. Our full compressing system reduced the size of memory needed by a factor of up to 63 at a cost of no more than a factor of 2 in the search effort.

This paper proposes an empirical approach for analyzing the rank distribution of relevant documents in Web search. From a methodological point of view a new transaction log analysis method is proposed; the relevance of documents is studied over transaction sessions rather than single transactions. From a practical point of view the paper provides insights about the actual rank distribution of relevant documents in Web search, with several consequences for the design of applications related to Web search.

Informally, a set of abstractions of a state space S is additive if the distance between any two states in S is always greater than or equal to the sum of the corresponding distances in the abstract spaces. The first known additive abstractions, called disjoint pattern databases, were experimentally demonstrated to produce state of the art performance on certain state spaces. However, previous applications were restricted to state spaces with special properties, which precludes disjoint pattern databases from being defined for several commonly used testbeds, such as Rubik's Cube, TopSpin and the Pancake puzzle. In this paper we give a general definition of additive abstractions that can be applied to any state space and prove that heuristics based on additive abstractions are consistent as well as admissible. We use this new definition to create additive abstractions for these testbeds and show experimentally that well chosen additive abstractions can reduce search time substantially for the (18,4)-TopSpin puzzle and by three orders of magnitude over state of the art methods for the 17-Pancake puzzle. We also derive a way of testing if the heuristic value returned by additive abstractions is provably too low and show that the use of this test can reduce search time for the 15-puzzle and TopSpin by roughly a factor of two.

QoS routing has been shown to be NP-hard. A recent study of its hardness shows that the "worst-case" may not occur in practice (Kuipers mieghem, 2003). This suggests that there may exist fast exact algorithms for the multi-constraint shortest path (MCSP) problem, an instance of QoS routing. Search techniques such as A* and IDA* may solve hard problems exactly in polynomial time. In Li et al. (2005), we deploy the idea of iterative deepening search to design IDA*_MCSP, and show its efficiency by extensive empirical study. In this paper, we show that for infeasible cases, where there is no feasible solution, IDA*_MCSP may not be as efficient as A*Prune. This motivates us to design an algorithm that is efficient in both feasible and infeasible cases. We design an exact MCSP algorithm A*_MCSP, which introduces the state notion and dominance relationship between states. Furthermore, we design an exact MCSP algorithm FringeMCSP. It can be regarded as an integration of IDA*_MCSP and A*_MCSP. Extensive empirical study shows that FringeMCSP has good performance in both feasible and infeasible cases; while IDA*_MCSP still shows its superiority among the proposed MCSP algorithms in feasible cases.

A pattern database (PDB) is a heuristic function implemented as a lookup table that stores the lengths of optimal solutions for subproblem instances. Standard PDBs have a distinct entry in the table for each subproblem instance. In this paper we investigate compressing PDBs by merging several entries into one, thereby allowing the use of PDBs that exceed available memory in their uncompressed form. We introduce a number of methods for determining which entries to merge and discuss their relative merits. These vary from domain-independent approaches that allow any set of entries in the PDB to be merged, to more intelligent methods that take into account the structure of the problem. The choice of the best compression method is based on domain-dependent attributes. We present experimental results on a number of combinatorial problems, including the four-peg Towers of Hanoi problem, the sliding-tile puzzles, and the Top-Spin puzzle. For the Towers of Hanoi, we show that the search time can be reduced by up to three orders of magnitude by using compressed PDBs compared to uncompressed PDBs of the same size. More modest improvements were observed for the other domains.

Association rule-based classifiers have recently emerged as competitive classification systems. However, there are still deficiencies that hinder their performance. One deficiency is the use of rules in the classification stage. Current systems assign classes to new objects based on the best rule applied or on some predefined scoring of multiple rules. In this paper we propose a new technique where the system automatically learns how to use the rules. We achieve this by developing a two-stage classification model. First, we use association rule mining to discover classification rules. Second, we employ another learning algorithm to learn how to use these rules in the prediction process. Our two-stage approach outperforms C4.5 and RIPPER on the UCI datasets in our study, and outperforms other rule- learning methods on more than half the datasets. The versatility of our method is also demonstrated by applying it to text classification, where it equals the performance of the best known systems for this task, SVMs.

This paper presents a parallel external-memory algorithm for performing a breadth-first traversal of an implicit graph on a cluster of workstations. The algorithm is a parallel version of the sorting-based external-memory frontier breadth-first traversal with delayed duplicate detection algorithm. The algorithm distributes the workload according to intervals that are computed at runtime via a sampling-based process. We present an experimental evaluation of the algorithm where we compare its performance to that of its sequential counterpart on the implicit graphs of two classic planning problems. The speedups attained by the algorithm over its sequential counterpart are consistently near linear and frequently above linear. Analysis reveals that the algorithm is proficient at distributing the workload and that increasing the number of samples obtained by the sampling-based process improves workload distribution. Analysis also reveals that the algorithm benefits from the caching of external memory in internal memory that is done by the operating system

Abstract — Energy efficiency is an important issue in multihop wireless networks with energy concerns. Usually it is achieved with accurate knowledge of the traffic pattern and/or the current network information such as the remaining energy level. We investigate the problem of designing a routing scheme to minimize the maximum energy utilization of a multihop wireless network with weak assumption of the traffic pattern and without ongoing collection of network information. We develop polynomial size LP models to design such a routing scheme. We discuss generalizations of the LP models to various radio transmission models. In an interference-limited scenario, we show how to guarantee schedulability of the oblivious routing. We present an extension to consider lossy links. We also discuss implementation issues. The LP models achieve performance close to what an oracle can achieve in the performance study. The results for multihop wireless networks with a single sink are especially good. We make a first stride in designing a traffic-oblivious energy-aware routing framework in multihop wireless networks. I.

QoS routing has been shown to be NP-hard. A recent study of its hardness suggests that the "worst-case" may not occur in practice, and thus there may exist a fast exact algorithm. We deploy the idea of iterative deepening search and look ahead to design an exact algorithm for finding the shortest path subject to multiple constraints (the MCSP problem). The accuracy of look-ahead information determines the efficiency of a search algorithm. The higher the accuracy of the look-ahead information, the more efficient the search process. An empirical study on a wide range of topologies shows the high accuracy of look-ahead information in the studied cases. Experimental results also show that our algorithm, IDA*/spl I.bar/MCSP, is fast and, in general, significantly outperforms A*Prune, an algorithm designed for the MCSP problem. The characteristics of iterative deepening search and the high accuracy of look-ahead information make IDA*/spl I.bar/MCSP a fast exact algorithm for the MCSP problem.

Applegate and Cohen (2003) computational complexity design demand oblivious routing schemes that achieve low oblivious ratio with no or approximate knowledge of traffic demands. We investigate the quality of oblivious routing with respect to path dispersion, which is concerned with the number of paths; and path variation, which is concerned with how far the paths are from the shortest paths and the variation of path lengths. The results show the dispersion and the variation are high in general. We propose a penalty method to improve the quality of oblivious routing. The penalty method strikes a good balance between the conflicting objectives of minimizing the oblivious ratio and optimizing the quality of oblivious routing. Moreover, we apply the simple penalty method to the problem of minimizing the maximum link utilization given a traffic matrix. With the penalty method, we can achieve almost the same maximum link utilization, and improve the quality of routing to almost perfect, i.e. one or two paths that are very close to the shortest paths between each pair of nodes.

Multihop wireless networks have unique features such as lossy links and interference. Both interference and lossy links affect the maximum achievable throughput of a network. Some wireless networks have energy constraints. Lossy links also affect energy efficiency due to retransmissions and broadcasting. We investigate the impact of lossy links on maximum achievable throughput and minimax energy utilization. These can be modeled as linear programming optimization problems. We give optimal solutions for both flow-based and destination-based routing. Experiments show that lossy links do have significant impact on the maximum achievable throughput. There are cases where a network can only achieve half of the throughput of the corresponding lossless network. The results show less significant impact of loss on energy efficiency. In some cases, the loss may be advantageous for energy efficiency, since the energy consumption may be reduced due to the loss of broadcasting messages. Experiments also show the significant impact of overhearing on energy efficiency.

Article Explicitly representing expected cost: an alternative to ROC representation Share on Authors: Chris Drummond School of Information Technology and Engineering, University of Ottawa, Ottawa, Ontario, Canada, K1N 6N5 School of Information Technology and Engineering, University of Ottawa, Ottawa, Ontario, Canada, K1N 6N5View Profile , Robert C. Holte School of Information Technology and Engineering, University of Ottawa, Ottawa, Ontario, Canada, K1N 6N5 School of Information Technology and Engineering, University of Ottawa, Ottawa, Ontario, Canada, K1N 6N5View Profile Authors Info & Claims KDD '00: Proceedings of the sixth ACM SIGKDD international conference on Knowledge discovery and data miningAugust 2000 Pages 198–207https://doi.org/10.1145/347090.347126Online:01 August 2000Publication History 110citation909DownloadsMetricsTotal Citations110Total Downloads909Last 12 Months44Last 6 weeks4 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

Locating software items is difficult, even for knowledgeable software designers, when searching in large, complex and continuously growing libraries. This paper describes a technique we term "active browsing". An active browser suggests to the designer items it estimates to be close to the target of the search. The novel aspect of active browsing is that it is entirely unobtrusive: it infers its similarity measure from the designer's normal browsing actions, without any special input. Experiments are presented in which the active browsing system succeeds 40% of the time in identifying the target before the designer has found it. An additional experiment indicates that this approach does, indeed, speed up searches.