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12
Compressing pattern databases
 In Proceedings of the Nineteenth National Conference on Artificial Intelligence (AAAI04
, 2004
"... A pattern database (PDB) is a heuristic function implemented as a lookup table that stores the lengths of optimal solutions for subproblem instances. Standard PDBs have a distinct entry in the table for each subproblem instance. In this paper we investigate compressing PDBs by merging several entrie ..."
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Cited by 45 (24 self)
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A pattern database (PDB) is a heuristic function implemented as a lookup table that stores the lengths of optimal solutions for subproblem instances. Standard PDBs have a distinct entry in the table for each subproblem instance. In this paper we investigate compressing PDBs by merging several entries into one, thereby allowing the use of PDBs that exceed available memory in their uncompressed form. We introduce a number of methods for determining which entries to merge and discuss their relative merits. These vary from domainindependent approaches that allow any set of entries in the PDB to be merged, to more intelligent methods that take into account the structure of the problem. The choice of the best compression method is based on domaindependent attributes. We present experimental results on a number of combinatorial problems, including the fourpeg Towers of Hanoi problem, the slidingtile puzzles, and the TopSpin puzzle. For the Towers of Hanoi, we show that the search time can be reduced by up to three orders of magnitude by using compressed PDBs compared to uncompressed PDBs of the same size. More modest improvements were observed for the other domains.
Maximizing over multiple pattern databases speeds up heuristic search
, 2006
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Duality in Permutation State Spaces and the Dual Search Algorithm
, 2007
"... Geometrical symmetries are commonly exploited to improve the efficiency of search algorithms. A new type of symmetry in permutation state spaces, duality, is introduced. Each state has a dual state. Both states share important attributes such as their distance to the goal. Given a state S, it is sho ..."
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Cited by 13 (10 self)
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Geometrical symmetries are commonly exploited to improve the efficiency of search algorithms. A new type of symmetry in permutation state spaces, duality, is introduced. Each state has a dual state. Both states share important attributes such as their distance to the goal. Given a state S, it is shown that an admissible heuristic of the dual state of S is an admissible heuristic for S. This provides opportunities for additional heuristic evaluations. An exact definition of the class of problems where duality exists is provided. A new search algorithm, dual search, is presented which switches between the original state and the dual state when it seems likely that the switch will improve the chance of reaching the goal faster. The decision of when to switch is very important and several policies for doing this are investigated. Experimental results show significant improvements for a number of applications, for using the dual state’s heuristic evaluation and/or dual search.
Predicting the Performance of IDA* using Conditional Distributions
, 2010
"... Korf, Reid, and Edelkamp introduced a formula to predict the number of nodes IDA* will expandon a single iteration for a given consistent heuristic, and experimentally demonstrated that it could make very accurate predictions. In this paper we show that, in addition to requiring the heuristic to be ..."
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Korf, Reid, and Edelkamp introduced a formula to predict the number of nodes IDA* will expandon a single iteration for a given consistent heuristic, and experimentally demonstrated that it could make very accurate predictions. In this paper we show that, in addition to requiring the heuristic to be consistent, their formula’s predictions are accurate only at levels of the bruteforce search tree where the heuristic values obey the unconditional distribution that they defined and then used in their formula. We then propose a new formula that works well without these requirements, i.e., it can make accurate predictions of IDA*’s performance for inconsistent heuristics and if the heuristic values in any level do not obey the unconditional distribution. In order to achieve this we introduce the conditional distribution of heuristic values which is a generalization of their unconditional heuristic distribution. We also provide extensions of our formula that handle individual start states and the augmentation of IDA* with bidirectional pathmax (BPMX), a technique for propagating heuristic values when inconsistent heuristics are used. Experimental results demonstrate the accuracy of our new method and all its variations.
Partial pattern databases
"... Abstract. Perimeters and pattern databases are two similar memorybased techniques used in singleagent search problems. We present partial pattern databases, which unify the two approaches into a single memorybased heuristic table. Our approach allows the use of any abstraction level. We achieve a t ..."
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Cited by 9 (1 self)
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Abstract. Perimeters and pattern databases are two similar memorybased techniques used in singleagent search problems. We present partial pattern databases, which unify the two approaches into a single memorybased heuristic table. Our approach allows the use of any abstraction level. We achieve a threefold reduction in the average number of nodes generated on the 13pancake puzzle and a 27 % reduction on the 15puzzle. 1
Predicting the Performance of IDA* with Conditional Distributions
, 2008
"... (Korf, Reid, and Edelkamp 2001) introduced a formula to predict the number of nodes IDA* will expand given the static distribution of heuristic values. Their formula proved to be very accurate but it is only accurate under the following limitations: (1) the heuristic must be consistent; (2) the pred ..."
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Cited by 4 (3 self)
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(Korf, Reid, and Edelkamp 2001) introduced a formula to predict the number of nodes IDA* will expand given the static distribution of heuristic values. Their formula proved to be very accurate but it is only accurate under the following limitations: (1) the heuristic must be consistent; (2) the prediction is for a large random sample of start states (or for large thresholds). In this paper we generalize the static distribution to a conditional distribution of heuristic values. We then propose a new formula for predicting the performance of IDA * that works well for inconsistent heuristics (Zahavi et al. 2007) and for any set of start states, not just a random sample. We also show how the formula can be enhanced to work well for single start states. Experimental results demonstrate the accuracy of our method in all these situations.
RelativeOrder Abstractions for the Pancake Problem
"... Abstract. The pancake problem is a famous search problem where the objective is to sort a sequence of objects (pancakes) through a minimal number of prefix reversals (flips). The best approaches for the problem are based on heuristic search with abstraction (pattern database) heuristics. We present ..."
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Abstract. The pancake problem is a famous search problem where the objective is to sort a sequence of objects (pancakes) through a minimal number of prefix reversals (flips). The best approaches for the problem are based on heuristic search with abstraction (pattern database) heuristics. We present a new class of abstractions for the pancake problem called relativeorder abstractions. Relativeorder abstractions have three advantages over the objectlocation abstractions considered in previous work. First, they are sizeindependent, i. e., do not need to be tailored to a particular instance size of the pancake problem. Second, they are more compact in that they can represent a larger number of pancakes within abstractions of bounded size. Finally, they can exploit symmetries in the problem specification to allow multiple heuristic lookups, significantly improving search performance over a single lookup. Our experiments show that compared to objectlocation abstractions, our new techniques lead to an improvement of one order of magnitude in runtime and up to three orders of magnitude in the number of generated states. 1