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.

In cooperative pathfinding problems, non-interfering paths that bring each agent from its current state to its goal state must be planned for multiple agents. We present the first practical, admissible, and complete algorithm for solving problems of this kind. First, we propose a technique called operator decomposition, which can be used to reduce the branching factors of many search algorithms, including algorithms for cooperative pathfinding. We then show how a type of independence common in instances of cooperative pathfinding problems can be exploited. Next, we take the idea of exploiting independent subproblems further by adding improvements that allow the algorithm to recognize many more cases of such independence. Finally, we show empirically that these techniques drastically improve the performance of the standard admissible algorithm for the cooperative pathfinding problem, and that their combination results in a complete algorithm capable of optimally solving relatively large problems in milliseconds.

Different solvers for computationally difficult problems such as satisfiability (SAT) perform best on different instances. Algorithm portfolios exploit this phenomenon by predicting solvers' performance on specific problem instances, then shifting computational resources to the solvers that appear best suited. This paper develops a new approach to the problem of making such performance predictions: natural generative models of solver behavior. Two are proposed, both following from an assumption that problem instances cluster into latent classes: a mixture of multinomial distributions, and a mixture of Dirichlet compound multinomial distributions. The latter model extends the former to capture burstiness, the tendency of solver outcomes to recur. These models are integrated into an algorithm portfolio architecture and used to run standard SAT solvers on competition benchmarks. This approach is found competitive with the most prominent existing portfolio, SATzilla, which relies on domain-specific, hand-selected problem features; the latent class models, in contrast, use minimal domain knowledge. Their success suggests that these models can lead to more powerful and more general algorithm portfolio methods.

However, there are many domains, work that is perhaps closest to ours is the "dead-end heuristic" such as map-based searches (common in GPS navigation, introduced by Björnsson and Halldórsson (2006). They computer games, and robotics) where the entire use a preprocessing phase to identify areas that are deadends, state-space is given explicitly. Optimal paths for such domains and create an abstract graph whose nodes are these can be found relatively quickly with simple heuristics, areas. Initially, the search is performed on the abstracted especially when compared to the time it takes to explore graph. The areas that were not visited during the search exponentially large combinatorial problems. Relative on the abstracted graph are then ignored when the search is quickness, however, might still not be fast enough in certain performed in the original search space. In addition to identifying real-time applications, where further improvement towards dead-ends, our approach also identifies (and prunes, high-speed performance is especially valued.

Perfect Information Monte Carlo (PIMC) search is a practical technique for playing imperfect information games that are too large to be optimally solved. Although PIMC search has been criticized in the past for its theoretical deficiencies, in practice it has often produced strong results in a variety of domains. In this paper, we set out to resolve this discrepancy. The contributions of the paper are twofold. First, we use synthetic game trees to identify game properties that result in strong or weak performance for PIMC search as compared to an optimal player. Second, we show how these properties can be detected in real games, and demonstrate that they do indeed appear to be good predictors of the strength of PIMC search. Thus, using the tools established in this paper, it should be possible to decide a priori whether PIMC search will be an effective approach to new and unexplored games.

State-of-the-art branch-and-bound algorithms for the maximum clique problem (Maxclique) frequently use an upper bound based on a partition P of a graph into independent sets for a maximum clique of the graph, which cannot be very tight for imperfect graphs. In this paper we propose a new encoding from Maxclique into MaxSAT and use MaxSAT technology to improve the upper bound based on the partition P. In this way, the strength of specific algorithms for Maxclique in partitioning a graph and the strength of MaxSAT technology in propositional reasoning are naturally combined to solve Maxclique. Experimental results show that the approach is very effective on hard random graphs and on DIMACS Maxclique benchmarks, and allows to close an open DIMACS problem.

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.

Depth-first proof-number search (df-pn) is powerful AND/OR tree search to solve positions in games. However, df-pn has a notorious problem of infinite loops when applied to domains with repetitions. Df-pn(r) cures it by ignoring proof and disproof numbers that may lead to infinite loops. This paper points out that df-pn(r) has a serious issue of underestimating proof and disproof numbers, while it also suffers from the overestimation problem occurring in directed acyclic graph. It then presents two practical solutions to these problems. While bypassing infinite loops, the threshold controlling algorithm (TCA) solves the underestimation problem by increasing the thresholds of df-pn. The source node detection algorithm (SNDA) detects the cause of overestimation and modifies the computation of proof and disproof numbers. Both TCA and SNDA are implemented on top of df-pn to solve tsume-shogi (checkmating problem in Japanese chess). Results show that df-pn with TCA and SNDA is far superior to df-pn(r). Our tsume-shogi solver is able to solve several difficult positions previously unsolved by any other solvers.

The depth first proof number search (df-pn) is an effective and popular algorithm for solving and-or tree problems by using proof and disproof numbers. This paper presents a simple but effective parallelization of the df-pn search algorithm for a shared-memory system. In this parallelization, multiple agents autonomously conduct the df-pn with a shared transposition table. For effective cooperation of agents, virtual proof and disproof numbers are introduced for each node, which is an estimation of future proof and disproof numbers by using the number of agents working on the node's descendants as a possible increase. Experimental results on large checkmate problems in shogi, which is a popular chess variant in Japan, show that reasonable increases in speed were achieved with small overheads in memory.

Search based solvers for Quantified Boolean Formulas (QBF) have adapted the SAT solver techniques of unit propagation and clause learning to prune falsifying assignments. The technique of cube learning has been developed to help them prune satisfying assignments. Cubes, however, have not been able to achieve the same degree of effectiveness as clauses. In this paper we demonstrate how a circuit representation for QBF can support the propagation of dual truth values. The dual values support the identical techniques of unit propagation and clause learning, except now it is satisfying assignments rather than falsifying assignments that are pruned. Dual value propagation thus exploits the circuit representation and the duality of QBF formulas so that the same effective SAT techniques can now be used to prune both falsifying and satisfyingly assignments. We show empirically that dual propagation yields significantperformance improvements and advances the state of the art in QBF solving.