We describe an online, interactive system with a graphical interface to illustrate the power and operation of consistency algorithms in a friendly and popular context, namely, solving Sudoku puzzles. Our tool implements algorithms for enforcing five (domain-based) consistency properties on binary and non-binary constraint models. Our tool is useful for research, education, and outreach. From a scientific standpoint, we propose a new consistency property that can solve the hardest known 9×9 Sudoku instances without search, but leave open the question of the lowest level of consistency needed to solve every 9×9 Sudoku puzzle. We have used the current tool and its predecessor in the classroom to introduce students to modeling problems with constraints, explain consistency properties, and illustrate the operations of constraint propagation and lookahead. Finally, we have also used this tool during outreach activities to demystify AI to children and the general public and show them how computers think.

Constraint propagation during backtrack search significantly improves the performance of solving a Constraint Satisfaction Problem. While Generalized Arc Consistency (GAC) is the most popular level of propagation, higher-level consistencies (HLC) are needed to solve difficult instances. Deciding to enforce an HLC instead of GAC remains the topic of active research. We propose a simple and effective strategy that reactively triggers an HLC by monitoring search performance: When search starts thrashing, we trigger an HLC, then conservatively revert to GAC. We detect thrashing by counting the number of backtracks at each level of the search tree and geometrically adjust the frequency of triggering an HLC based on its filtering effectiveness. We validate our approach on benchmark problems using Partition-One Arc-Consistency as an HLC. However, our strategy is generic and can be used with other higher-level consistency algorithms.

We propose to exploit cycles in the constraint network of a Constraint Satisfaction Problem (CSP) to vehicle constraint propagation and improve the effectiveness of local consistency algorithms. We focus our attention on the consistency property Partition-One Arc-Consistency (POAC), which is a stronger variant of Singleton Arc-Consistency (SAC). We modify the algorithm for enforcing POAC to operate on a minimum cycle basis (MCB) of the incidence graph of the CSP. We empirically show that our approach improves the performance of problem solving and constitutes a novel and effective localization of consistency algorithms. Although this paper focuses on POAC, we believe that exploiting cycles, such as MCBs, is applicable to other consistency algorithms and that our study opens a new direction in the design of consistency algorithms. This research is documented in a technical report (Woordward, Choueiry, and Bessiere 2016). http://consystlab.unl.edu/our_work/StudentReports/TR-UNL-CSE-2016-0004.pdf

In Constraint Processing, many algorithms for enforcing the same level of local consistency may exist. The performance of those algorithms varies widely. In order to understand what problem features lead to better performance of one algorithm over another, we utilize an algorithm configurator to tune the parameters of a random problem generator and maximize the performance difference of two consistency algorithms for enforcing constraint minimality. Our approach allowed us to generate instances that run 1000 times faster for one algorithm over the other.

Computing the minimal network of a Constraint Satisfaction Problem (CSP) is a useful and difficult task. Two algorithms, PerTuple and AllSol, were proposed to this end. The performances of these algorithms vary with the problem instance. We use Machine Learning techniques to build a classifier that predicts which of the two algorithms is likely to be more effective.

The tractability of a Constraint Satisfaction Problem (CSP)is guaranteed by a direct relationship between its consistencylevel and a structural parameter of its constraint network suchas the treewidth. This result is not widely exploited in practicebecause enforcing higher-level consistencies can be costlyand can change the structure of the constraint network andincrease its width. Recently, R(*,m)C was proposed as a relational consistency property that does not modify the structureof the graph and, thus, does not affect its width. In this paper,we explore two main strategies, based on a tree decomposition of the CSP, for improving the performance of enforcingR(*,m)C and getting closer to the above tractability condition. Those strategies are: a) localizing the application ofthe consistency algorithm to the clusters of the tree decomposition, and b) bolstering constraint propagation betweenclusters by adding redundant constraints at their separators,for which we propose three new schemes. We characterizethe resulting consistency properties by comparing them, theoretically and empirically, to the original R(*,m)C and thepopular GAC and maxRPWC, and establish the benefits ofour approach for solving difficult problems.

Freuder and Elfe (1996) introduced Neighborhood Inverse Consistency (NIC) as a strong local consistency property for binary CSPs. While enforcing NIC can significantly filter the variables domains, the proposed algorithm is too costly to be used on dense graphs or for lookahead during search. In this paper, we introduce and characterize Relational Neighborhood Inverse Consistency (RNIC) as a local consistency property that operates on the dual graph of a non-binary CSP. We describe and characterize a practical algorithm for enforcing it. We argue that defining RNIC on the dual graph unveils unsuspected opportunities to reduce the computational cost of our algorithm and increase its filtering effectiveness. We show how to achieve those effects by modifying the topology of the dual graph, yielding new variations the RNIC property. We also introduce an adaptive strategy to automatically select the appropriate property to enforce given the connectivity of the dual graph. We integrate the resulting techniques as full lookahead strategies in a backtrack search procedure for solving CSPs, and demonstrate the effectiveness of our approach for solving known difficult benchmark problems.

Freuder and Elfe (1996) introduced Neighborhood Inverse Consistency (NIC) for binary CSPs. In this paper, we introduce RNIC, the extension of NIC to non-binary CSPs, and describe a practical algorithm for enforcing it. We propose an adaptive strategy to weaken or strengthen this property based on the connectivity of the network. We demonstrate the effectiveness of RNIC as a full lookahead strategy during search for solving difficult benchmark problems.

Consistency properties and algorithms for achieving them are at the heart of the success of Constraint Programming. In this paper, we study the relational consistency property R(*,m)C, which is equivalent to m-wise consistency proposed in relational databases. We also define wR(*,m)C, a weaker variant of this property. We propose an algorithm for enforcing these properties on a Constraint Satisfaction Problem by tightening the existing relations and without introducing new ones. We empirically show that wR(*,m)C solves in a backtrack-free manner all the instances of some CSP benchmark classes, thus hinting at the tractability of those classes.

The building identification (BID) problem is based on a pro-cess that uses publicly available information to automati-cally assign addresses to buildings in satellite imagery. In previous work, we have shown the advantages of casting the BID problem as a Constraint Satisfaction Problem (CSP) using the same generic constraint-model to represent all problem instances. However, a generic model is unable to represent with the necessary precision the addressing varia-tions throughout the world, limiting the applicability of our previous approach. In this paper, we describe the end-to-end process used to solve the BID with a new model-generation technique that uses instance-specific information to auto-matically infer a representative constraint model of the BID. This inferred model is used by our custom constraint solver to identify buildings in satellite imagery more efficiently and with higher precision than using a single model. We evalu-ate our approach on El Segundo California, and empirically demonstrate its effectiveness for geographic areas larger than previously tested. We conclude with a discussion of the gen-erality of our approach, and present directions for future work.

We address the problem of detecting execution errors in communication protocols. A communication protocol is modeled as or finite state machine (FSM) that can be used as an external observer for detecting execution errors. Wang and Schwartz (1992, 1993) introduce the concept of multiple observers obtained by an adequate decomposition of the FSM. We first address the decomposition procedure from the perspective of error control codes and show that the decomposition algorithm can be restated as a simple state coding algorithm. Then, we discuss the features of fault tolerance of the resulting decomposition. We generalize the concept of multiple observers into the one of fault tolerant multiple observers. A set of observers is said to be fault tolerant if it is capable of detecting the execution errors of a protocol even when a subset of the observers is faulty. We show that error control codes can be used to generate multiple observers that are fault tolerant. We illustrate our approach on the ISO transport protocol class 4 (TP4). Finally, we give some hints on how to assign codes to the states while maximizing the fault coverage of the resulting decomposition.

Abstraction is a useful technique for reducing complexity in problem solving. In this paper, the authors present two abstraction techniques and one partitioning heuristic to solve resource allocation problems. The partitioning heuristic decomposes the resource allocation problem into easy and difficult components competing for pools of resources. A hierarchy of resource pools allows conflict resolution to occur at the most appropriate level of abstraction. The temporal abstraction techniques simplify the decoupled components. They also aid the user in assessing the tightness of the problem and the types of missing resources. There are two main advantages to using the abstractions the authors propose: they rapidly provide a first solution which can be refined given more computation time, and they provide an explanation in terms of missing resources if the resource allocation problem is unsolvable.