HDA* is a simple, parallelization of A* where work is asynchronously distributed among the nodes by a global hash function. Using up to 1024 cores on a large distributed memory cluster, we evaluate HDA* for a domain-independent planner as well an application-specific 24-puzzle solver. We show that HDA* scales fairly well on a large cluster using up to 1024 cores. Our analysis of the scaling behavior shows that on a cluster of multicore nodes, using only a subset of the available cores and leaving some cores idle can, surprisingly, lead to better results.

search algorithms such as IDA* or heuristic-search planners. Our method aims to generate a strong heuristic from a given weak heuristic h 0 through bootstrapping. The "easy" problem instances that can be solved using h 0 provide training examples for a learning algorithm that produces a heuristic h 1 that is expected to be stronger than h 0 . If h 0 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 h 0 . The bootstrap process is then repeated using h i in lieu of h i –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.

True distance memory-based heuristics (TDHs) were recently introduced as a way to obtain admissible heuristics for explicit state spaces. In this paper, we introduce a new TDH, the portal-based heuristic. The domain is partitioned into regions and portals between regions are identified. True distances between all pairs of portals are stored and used to obtain admissible heuristics throughout the search. We introduce an A*-based algorithm that takes advantage of the special properties of the new heuristic. We study the advantages and limitations of the new heuristic. Our experimental results show large performance improvements over previously-reported TDHs for commonly used classes of maps.

We present a new heuristic point-to-point shortest path algorithm based on contraction hierarchies (CH). Given an epsilon >= 0, we can prove that the length of the path computed by our algorithm is at most (1 + ε) times the length of the optimal (shortest) path. Exact CH is based on node contraction: removing nodes from a network and adding shortcuts to preserve shortest path distances. Our heuristic CH tries to avoid adding shortcuts even when a replacement path is (1+epsilon) times longer. However, we cannot avoid all such shortcuts, as we need to ensure that errors do not stack. Combinations with goal-directed techniques bring further speed-ups.

In this paper we improve solving two-player games by computing the game-theoretical value of every reachable state. A graphics processing unit located on the graphics card is used as a co-processor to accelerate the solution process. We exploit perfect hash functions to store the game states efficiently in memory and to transfer their ordinal representation between the host and the graphics card. As an application we validate Gasser's results that Nine-Men-Morris is a draw on a personal computer. Moreover, our solution is strong, while for the opening phase Gasser only provided a weak solution.

For problems such as pathfinding in video games and robotics, a search algorithm must be real-time (return the next move within a fixed time bound) and dynamic (accommodate edge costs that can increase and decrease before the goal is reached). Existing real-time search algorithms, such as LSS-LRTA*, can handle edge cost increases but do not handle edge cost decreases. Existing dynamic search algorithms, such as D* Lite, are not real-time. We show how these two families of algorithms can be combined using bidirectional search, producing Real-Time D* (RTD*), the first real-time search algorithm designed for dynamic worlds. Our empirical evaluation shows that, for dynamic grid pathfinding, RTD* results in significantly shorter trajectories than either LSS-LRTA* or naive real-time adaptations of D* Lite because of its ability to opportunistically exploit shortcuts.

Transposition tables are a well-known method for pruning duplicates in heuristic search. This paper presents a detailed analysis of transposition tables for IDA*. We show that some straightforward implementations of IDA* with transposition tables (IDA*+TT) can result in suboptimal solutions being returned. Furthermore, straightforward implementations of IDA*+TT are not complete. We identify several variants of IDA*+TT which are guaranteed to return the optimal solution, as well as a complete variant. An empirical study shows that IDA*+TT can significantly improve upon the performance of A* in domain-independent planning.

Memory-based heuristic techniques have been used to effectively reduce search times in implicit graphs. Recently, these techniques have been applied to improving search times in explicit graphs. This paper presents a new memory-based, additive heuristic that can be used on a type of explicit graph: the four-connected gridworld. The heuristic reduces the number of expanded nodes by up to five times, reduces execution time by up to 29 times, and can efficiently accommodate graph changes.

A key factor that can dramatically reduce the search space during constraint solving is the criterion under which the variable to be instantiated next is selected. For this purpose numerous heuristics have been proposed. Some of the best of such heuristics exploit information about failures gathered throughout search and recorded in the form of constraint weights, while others measure the importance of variable assignments in reducing the search space. In this work we experimentally evaluate the most recent and powerful variable ordering heuristics, and new variants of them, over a wide range of benchmarks. Results demonstrate that heuristics based on failures are in general more efficient. Based on this, we then derive new revision ordering heuristics that exploit recorded failures to efficiently order the propagation list when arc consistency is maintained during search. Interestingly, in addition to reducing the number of constraint checks and list operations, these heuristics are also able to cut down the size of the explored search tree.