Dots-And-Boxes is a well-known and widely-played combinatorial game. While the rules of play are very simple, the state space for even very small games is extremely large, and finding the outcome under optimal play is correspondingly hard. In this paper we introduce a Dots-And-Boxes solver which is significantly faster than the current state-of-the-art: over an order-of-magnitude faster on several large problems. Our approach uses Alpha-Beta search and applies a number of techniques---both problem-specific and general---that reduce the search space to a manageable size. Using these techniques, we have determined for the first time that Dots-And-Boxes on a board of 4 x 5 boxes is a tie given optimal play; this is the largest game solved to date.

This paper is devoted to sequential decision making with Rank Dependent expected Utility (RDU). This decision criterion generalizes Expected Utility and enables to model a wider range of observed (rational) behaviors. In such a sequential decision setting, two conflicting objectives can be identified in the assessment of a strategy: maximizing the performance viewed from the initial state (optimality), and minimizing the incentive to deviate during implementation (deviation-proofness). In this paper, we propose a minimax regret approach taking these two aspects into account, and we provide a search procedure to determine an optimal strategy for this model. Numerical results are presented to show the interest of the proposed approach in terms of optimality, deviation-proofness and computability.

The cost of an optimal delete relaxed plan, known as h+, is a powerful admissible heuristic but is in general intractable to compute. In this paper we examine the problem of computing h+ by encoding it as a MAXSAT problem. We develop a new encoding that utilizes constraint generation to support the computation of a sequence of increasing lower bounds on h+. We show a close connection between the computations performed by a recent approach for solving MAXSAT and a hitting set approach recently proposed for computing h+. Using this connection we observe that our MAXSAT computation can be initialized with a set of landmarks computed by LM-cut. By judicious use of MAXSAT solving along with a technique of lazy heuristic evaluation we obtain speedups for finding optimal plans over LM-cut on a number of domains. Our approach enables the exploitation of continued progress in MAXSAT solving, and also makes it possible to consider computing or approximating heuristics that are even more informed that h+ by, for example, adding some information about deletes back into the encoding.

High dimensional nearest neighbor search is a fundamental problem and has found applications in many domains. Although many hashing based approaches have been proposed for approximate nearest neighbor search in high dimensional space, one main drawback is that they often return many false positives that need to be filtered out by a post procedure. We propose a novel method to address this limitation in this paper. The key idea is to introduce a filtering procedure within the search algorithm, based on the compressed sensing theory, that effectively removes the false positive answers. We first obtain a sparse representation for each data point by the landmark based approach, after which we solve the nearly duplicate search that the difference between the query and its nearest neighbors forms a sparse vector living in a small ℓp ball, where p ≤ 1. Our empirical study on real-world datasets demonstrates the effectiveness of the proposed approach compared to the state-of-the-art hashing methods.

Although successfully employed on many industrial problems, Combinatorial Optimization still has limited applicability on several real-world domains, often due to modeling difficulties. This is typically the case for systems under the control of an on-line policy: even when the policy itself is well known, capturing its effect on the system in a declarative model is often impossible by conventional means. Such a difficulty is at the root of the classical, sharp separation between off- line and on-line approaches. In this paper, we investigate a general method to model controlled systems, based on the integration of Machine Learning and Constraint Programming (CP). Specifically, we use an Artificial Neural Network (ANN) to learn the behavior of a controlled system (a multicore CPU with thermal con- trollers) and plug it into a CP model by means of Neuron Constraints. The method obtains significantly better results compared to an approach with no ANN guidance. Neuron Constraints were first introduced in [Bartolini et al., 2011b] as a mean to model complex systems: providing evidence of their applicability to controlled systems is a significant step forward, broadening the application field of combinatorial methods and disclosing opportunities for hybrid off-line/on-line optimization.

Homotopy classes of trajectories, arising due to the presence of obstacles, are defined as sets of trajectories that can be transformed into each other by gradual bending and stretching without colliding with obstacles. The problem of exploring/finding the different homotopy classes in an environment and the problem of finding least-cost paths restricted to a specific homotopy class (or not belonging to certain homotopy classes) arises frequently in such applications as predicting paths for unpredictable entities and deployment of multiple agents for efficient exploration of an environment. In [Bhattacharya, Kumar, Likhachev, AAAI 2010] we have shown how homotopy classes of trajectories on a two-dimensional plane with obstacles can be classified and identified using the Cauchy Integral Theorem and the Residue Theorem from Complex Analysis. In more recent work [Bhattacharya, Likhachev, Kumar, RSS 2011] we extended this representation to three-dimensional spaces by exploiting certain laws from the Theory of Electromagnetism (Biot-Savart law and Ampere's Law) for representing and identifying homotopy classes in three dimensions in an efficient way. Using such a representation, we showed that homotopy class constraints can be seamlessly weaved into graph search techniques for determining optimal path constrained to certain homotopy classes or forbidden from others, as well as for exploring different homotopy classes in an environment. (This is a condensed, non-technical overview of work previously published in the proceedings of Robotics: Science and Systems, 2011 conference [Bhattacharya, Likhachev, Kumar, RSS 2011].)

Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful cases: symmetry breaking constraints for row and column symmetry, and symmetry breaking constraints for eliminating value symmetry.

In the multi agent path finding problem (MAPF) paths shouldbe found for several agents, each with a different start andgoal position such that agents do not collide. Previous optimalsolvers applied global A*-based searches. We presenta new search algorithm called Conflict Based Search (CBS).CBS is a two-level algorithm. At the high level, a search isperformed on a tree based on conflicts between agents. At thelow level, a search is performed only for a single agent at atime. In many cases this reformulation enables CBS to examinefewer states than A* while still maintaining optimality.We analyze CBS and show its benefits and drawbacks. Experimentalresults on various problems shows a speedup ofup to a full order of magnitude over previous approaches.

A* is the algorithm of finding the shortest path between two nodes in a graph. When the searching problem is constituted of a set of linked graphs, A* searches solution like if it is face of one graph formed by linked graphs. While researchers have developed solutions to reduce the execution time of A* in multiple cases by multiples techniques, we develop a new algorithm: DEC-A* which is a decentralized version of A* composing a solution through a collection of graph. A* uses a distance-plus-cost heuristic function to determine the order in which the search visits nodes in the tree. Our algorithm DEC-A* extends the evaluation of the distance-plus-cost heuristic to be the sum of two functions : local distance, which evaluates the cost to reach the nearest neighbor node s to the goal, and global distance which evaluates the cost from s to the goal through other graphs. DEC-A* reduces the time of finding the shortest path and reduces the complexity, while ensuring the privacy of graphs.

The Model AI Assignments session seeks to gather and disseminate the best assignment designs of the Artificial Intelligence (AI) Education community. Recognizing that assignments form the core of student learning experience, we here present abstracts of three AI assignments from the 2012 session that are easily adoptable, playfully engaging, and flexible for a variety of instructor needs.