We propose a branch-and-bound algorithm for robust rigid registration of two point clouds in the presence of a large number of outlier correspondences. For this purpose, we consider a maximum consensus formulation of the registration problem and reformulate it as a (large) maximal clique search in a correspondence graph, where a clique represents a complete rigid transformation. Specifically, we use a maximum clique algorithm to enumerate large maximal cliques and a fitness procedure that evaluates each clique by solving a least-squares optimization problem. The main advantages of our approach are 1) it is possible to exploit the cutting-edge optimization techniques employed by current exact maximum clique algorithms, such as partial maximum satisfiability-based bounds, branching by partitioning or the use of bitstrings, etc.; 2) the correspondence graphs are expected to be sparse in real problems (confirmed empirically in our tests), and, consequently, the maximum clique problem is expected to be easy; 3) it is possible to have agoodcontrol of suboptimality with a k-nearest neighbor analysis that determines the size of the correspondence graph as a function of$k$. The new algorithm is calledCliRegand has been implemented in C++. To evaluateCliReg, we have carried out extensive tests both on synthetic and real public datasets. The results show thatCliRegclearly dominates the state of the art (e.g.,RANSAC,FGR, andTEASER++) in terms of robustness, with a running time comparable toTEASER++andRANSAC. In addition, we have implemented a fast variant calledCliRegMutualthat performs similarly to the fastest heuristicFGR.

This paper presents a robust solution to the mobile robotics data association problem based on solving the maximum clique problem (MCP) in a typically sparse correspondence graph, which contains compatibility information between pairs of observations and landmarks. Bit sparse optimizations are designed and implemented in a new algorithm BBMCS, which reduces computation and memory requirements of a leading general purpose maximum clique solver, to make it possibly the best exact sparse MCP algorithm currently found in the literature. BBMCS is reported to achieve very good results in terms of robustness with few assumptions on noise and visibility, while managing very reasonable computation time and memory usage even for complex large data association problems.

We present a new implicit branching strategy for maximum clique. The new strategy is based in Konj and Janečič's improvement over reference MCR algorithm. It uses a fixed initial non increasing degree vertex ordering at every step of the search, to obtain tighter bounds than MCR on average. We show that the new branching strategy integrates nicely with a natural bit model for the domain. This allows for efficient bound computing using bit masking operations, so that overall improvement in performance is achieved. We present empirical validation over structured and random graphs.

This paper presents a general purpose methodology to derive new heuristics for constraint satisfaction problems using the information contained in an auxiliary graph. The method is then applied to implement a powerful heuristic for Sudoku which is ‘almost perfect’ in the sense that a depth first search procedure needs very few backtracks to solve the 16x16 puzzle. The heuristic uses a least-constraining tie break for variable ordering, something very unusual in CSP domains. The paper also presents a minimal set of logical rules which the authors conjecture to solve all 9x9 Sudoku grids with unique solution with just one level of recursion at most.

This paper presents two new exact general purpose bit-parallel algorithms (BB-SAT and BBP-SAT) for the Boolean satisfiability problem (SAT). Based on the authors' recent successful bit-parallel algorithm for the maximum clique problem, the SAT formula is first reduced to a directed graph which is then bit encoded. As a result, search traverses a bit vector graph space. At present the encoding allows for an efficient bitwise computation of graph state transitions as well as unit clause and pure literal evaluation. Experiments carried out on a number of DIMACS instances are highly encouraging since BBP-SAT is already reasonably competitive employing just basic DPLL tactics with minor refinements. BBP-SAT is a fresh approach in an otherwise mature domain. Further additional bit encoded knowledge of the more recent successful SAT algorithms (e.g. bit parallel heuristic variable selection) should make BBP-SAT a competitive general purpose solver.

Recently, a novel solution to the Simultaneous Localization and Map building (SLAM) problem for complex indoor environments was presented, using a set of splines for describing the geometries detected by a laser range finder mounted on a mobile platform. In this paper, a method for exploiting the geometric information underlying in these maps in the data association process is described. The proposed approach uses graphs of relations between simple features extracted from the environment, and a bit encoded implementation for obtaining a maximum clique that relates observations with previously visited areas. This information is used to update the relative positions of a collage of submaps of limited size.

It is the authors' belief that the ability of processors to compute bit parallel operations should have a right to exist as an optimization discipline, rather than a state-of- the-art technique. This paper is a step forward in this direction analysing a number of key issues related to bit model design and implementation of search problems. Building efficient search algorithms optimized at bit level is a difficult task It requires not only a good implementation but also an adequate model so as to make bitwise operations meaningful, and only by addressing design and implementation globally an improvement in efficiency can be obtained. On the other hand, we have proved in this paper that the improvement can conceivably be exponential on the size of the CPU register for problems in NP. This global approach has been used to implement the fastest complete algorithm, to the best of our knowledge, for the maximum clique problem, an important NP-hard combinatorial problem from the graph domain. Our solver clearly outperforms other existing algorithms for hard instances, in some cases by nearly an order of magnitude.

This paper shows a way to speed up search by using an encoding at bit level to model a particular domain. A bitboard is an unsigned integer whose bits have been given an interpretation in the world of discourse. In models encoded in such a way, states will be described internally as a set of bitboard tuples, whilst operators which allow for transitions between states are essentially bitwise operations over elements belonging to that set. Given a 64-bit processor word, for each transition it would be theoretically possible to reach another state 64 times faster than with a normal encoding, fast transitions being one of the main issues for efficient search algorithms. We have analysed some other key issues related to efficient bitboard model design and formalised the concepts of well formed heuristics and bitboard guides. We have used this approach to solve instances of the maximum clique problem thus increasing the performance of one of the fastest algorithms known in the domain for optimal search