Depth-first iterative-deepening: an optimal admissible tree search
Artificial Intelligence
Artificial intelligence: a theoretical approach
Artificial intelligence: a theoretical approach
Sorting with fixed-length reversals
Discrete Applied Mathematics - Special volume on computational molecular biology
Disjoint pattern database heuristics
Artificial Intelligence - Chips challenging champions: games, computers and Artificial Intelligence
Machine Discovery of Effective Admissible Heuristics
Machine Learning
Searching with Pattern Databases
AI '96 Proceedings of the 11th Biennial Conference of the Canadian Society for Computational Studies of Intelligence on Advances in Artificial Intelligence
Maximizing over multiple pattern databases speeds up heuristic search
Artificial Intelligence
Dual search in permutation state spaces
AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
Genome rearrangement and planning
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 3
New admissible heuristics for domain-independent planning
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 3
Domain-independent construction of pattern database heuristics for cost-optimal planning
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
Additive pattern database heuristics
Journal of Artificial Intelligence Research
Dual lookups in pattern databases
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Finding optimal solutions to the twenty-four puzzle
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 2
Finding optimal solutions to Rubik's cube using pattern databases
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Hierarchical A *: searching abstraction hierarchies efficiently
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Hierarchical heuristic search revisited
SARA'05 Proceedings of the 6th international conference on Abstraction, Reformulation and Approximation
Solving the 24 puzzle with instance dependent pattern databases
SARA'05 Proceedings of the 6th international conference on Abstraction, Reformulation and Approximation
Optimal admissible composition of abstraction heuristics
Artificial Intelligence
Relative-Order Abstractions for the Pancake Problem
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Implicit abstraction heuristics
Journal of Artificial Intelligence Research
Inconsistent heuristics in theory and practice
Artificial Intelligence
Learning heuristic functions for large state spaces
Artificial Intelligence
Landmark-enhanced abstraction heuristics
Artificial Intelligence
Bridging the gap between refinement and heuristics in abstraction
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Getting the most out of pattern databases for classical planning
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Informally, a set of abstractions of a state space S is additive if the distance between any two states in S is always greater than or equal to the sum of the corresponding distances in the abstract spaces. The first known additive abstractions, called disjoint pattern databases, were experimentally demonstrated to produce state of the art performance on certain state spaces. However, previous applications were restricted to state spaces with special properties, which precludes disjoint pattern databases from being defined for several commonly used testbeds, such as Rubik's Cube, TopSpin and the Pancake puzzle. In this paper we give a general definition of additive abstractions that can be applied to any state space and prove that heuristics based on additive abstractions are consistent as well as admissible. We use this new definition to create additive abstractions for these testbeds and show experimentally that well chosen additive abstractions can reduce search time substantially for the (18,4)-TopSpin puzzle and by three orders of magnitude over state of the art methods for the 17-Pancake puzzle. We also derive a way of testing if the heuristic value returned by additive abstractions is provably too low and show that the use of this test can reduce search time for the 15-puzzle and TopSpin by roughly a factor of two.