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15
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.
Hierarchical heuristic search revisited
 In Abstraction, Reformulation and Approximation
, 2005
"... Abstract. Pattern databases enable difficult search problems to be solved very quickly, but are large and timeconsuming to build. They are therefore best suited to situations where many problem instances are to be solved, and less than ideal when only a few instances are to be solved. This paper ex ..."
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Abstract. Pattern databases enable difficult search problems to be solved very quickly, but are large and timeconsuming to build. They are therefore best suited to situations where many problem instances are to be solved, and less than ideal when only a few instances are to be solved. This paper examines a technique hierarchical heuristic searchespecially designed for the latter situation. The key idea is to compute, on demand, only those pattern database entries needed to solve a given problem instance. Our experiments show that Hierarchical IDA * can solve individual problems very quickly, up to two orders of magnitude faster than the time required to build an entire highperformance pattern database. 1
A general theory of additive state space abstractions
 JAIR
"... 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 ..."
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Cited by 23 (13 self)
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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 17Pancake 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 15puzzle and TopSpin by roughly a factor of two. 1.
Algorithmic Approaches for Genome Rearrangement: A Review
 IEEE Trans. Systems, Man, and Cybernetics
, 2006
"... Abstract—Genome rearrangement is a new and important research area that studies the gene orders and the evolution of gene families. With the development of fast sequencing techniques, largescale DNA molecules are investigated with respect to the relative order of genes in them. Contrary to the trad ..."
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Abstract—Genome rearrangement is a new and important research area that studies the gene orders and the evolution of gene families. With the development of fast sequencing techniques, largescale DNA molecules are investigated with respect to the relative order of genes in them. Contrary to the traditional alignment approach, genome rearrangements are based on comparison of gene orders. Recently, it became a topic capturing wide attention. In this paper, we cover many kinds of rearrangement events such as reversal, transposition, translocation, fussion, fission, andsoon. Different types of distances between genomes or chromosomes are discussed. A variety of mathematic models are included. Index Terms—Genome rearrangement, reversal, syntenic distance, translocation, transposition. I.
Genomic sorting with lengthweighted reversals
 Genome Informatics
, 2002
"... Current algorithmic studies of genome rearrangement ignore the length of reversals (or inversions); rather, they only count their number. We introduce a new cost model in which the lengths of the reversed sequences play a role, allowing more flexibility in accounting for mutation phenomena. Our focu ..."
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Current algorithmic studies of genome rearrangement ignore the length of reversals (or inversions); rather, they only count their number. We introduce a new cost model in which the lengths of the reversed sequences play a role, allowing more flexibility in accounting for mutation phenomena. Our focus is on sorting unsigned (unoriented) permutations by reversals; since this problem remains difficult (NPhard) in our new model, the best we can hope for are approximation results. We propose an efficient, novel algorithm that takes (a monotonic function f of) length into account as an optimization criterion and study its properties. Our results include an upper bound of O(f(n) lg 2 n) for any additive cost measure f on the cost of sorting any nelement permutation, and a guaranteed approximation ratio of O(lg 2 n) times optimal for sorting a given permutation. Our work poses some interesting questions to both biologists and computer scientists and suggests some new bioinformatic insights that are currently being studied.
Sorting by lengthweighted reversals: Dealing with signs and circularity
 Proc. of the Fifteenth Annual Combinatorial Pattern Matching Symposium, volume 3109 of Lecture Notes in Computer Science
, 2004
"... Abstract. We consider the problem of sorting linear and circular permutations and 0/1 sequences by reversals in a lengthsensitive cost model. We extend the results on sorting by lengthweighted reversals in two directions: we consider the signed case for linear sequences and also the signed and uns ..."
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Cited by 4 (1 self)
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Abstract. We consider the problem of sorting linear and circular permutations and 0/1 sequences by reversals in a lengthsensitive cost model. We extend the results on sorting by lengthweighted reversals in two directions: we consider the signed case for linear sequences and also the signed and unsigned cases for circular sequences. We give lower and upper bounds as well as guaranteed approximation ratios for these three cases. The main result in this paper is an optimal polynomialtime algorithm for sorting circular 0/1 sequences when the cost function is additive. 1
Solving games in parallel with lineartime perfect hash functions
, 2009
"... In this paper, we propose an efficient method of solving one and twoplayer combinatorial games by mapping each state to a unique bit in memory. In order to avoid collisions, a concise portfolio of perfect hash functions is provided. Such perfect hash functions then address tables that serve as a ..."
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In this paper, we propose an efficient method of solving one and twoplayer combinatorial games by mapping each state to a unique bit in memory. In order to avoid collisions, a concise portfolio of perfect hash functions is provided. Such perfect hash functions then address tables that serve as a compressed representation of the search space and support the execution of exhaustive search algorithms like breadthfirst search and retrograde analysis. Perfect hashing computes the rank of a state, while the inverse operation unrank reconstructs the state given its rank. Efficient algorithms are derived, studied in detail and generalized to a larger variety of games. We study rank and unrank functions for permutation games with distinguishable pieces, for selection games with indistinguishable pieces, and for general reachability sets. The running time for ranking and unranking in all three cases is linear in the size of the state vector. To overcome space and time limitations in solving previously unsolved games like FrogsandToads and FoxandGeese, we utilize parallel computing power in form of multiple
A FAST ALGORITHM FOR SORTING BY SHORT SWAP
, 2006
"... A short swap is an operation that switches two elements that have at most one element in between. In this paper, we consider the problem of sorting an arbitrary permutation by short swaps. We give an algorithm which sorts any permutation of length n within (3/16)n 2 +O(n log n) steps, improving the ..."
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A short swap is an operation that switches two elements that have at most one element in between. In this paper, we consider the problem of sorting an arbitrary permutation by short swaps. We give an algorithm which sorts any permutation of length n within (3/16)n 2 +O(n log n) steps, improving the previous (5/24)n 2 +O(n log n) upper bound.
Models of active learning in groupstructured state spaces ⋆
"... We investigate the problem of learning the transition dynamics of deterministic, discretestate environments. We assume that an agent exploring such an environment is able to perform actions (from a finite set of actions) in the environment and to sense the state changes. The question investigated i ..."
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We investigate the problem of learning the transition dynamics of deterministic, discretestate environments. We assume that an agent exploring such an environment is able to perform actions (from a finite set of actions) in the environment and to sense the state changes. The question investigated is whether the agent can learn the dynamics without visiting all states. Such a goal is unrealistic in general, hence we assume that the environment has structural properties an agent might exploit. In particular, we assume that the set of all action sequences forms an algebraic group. We introduce a learning model in different variants and study under which circumstances the corresponding “group structured environments ” can be learned efficiently by experimenting with group generators (actions). It turns out that for some classes of such environments the choice of actions given to the agent determines if efficient learning is possible. Negative results are presented, even without efficiency constraints, for rather general classes of groups, showing that even with group structure, learning an environment from partial information is far from trivial. However, positive results for special subclasses of Abelian groups turn out to be a good starting point for the design of efficient learning algorithms based on structured representations. Key words: learning theory, active learning, groups, algebraic structures ⋆ This paper is an extended version of [3].