Heuristic Methods for Hypertree Decomposition

Dermaku, Artan; Ganzow, Tobias; Gottlob, Georg; Mcmahan, Ben; Musliu, Nysret; Samer, Marko

doi:10.1007/978-3-540-88636-5_1

Cited by 33 publications

(38 citation statements)

References 14 publications

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“…Dermaku et al [2] used heuristics for generating tree decompositions and partitioning hypergraphs to produce hypertree decompositions. Harvey et al [11] introduced the reduced normal form of a hypertree decomposition and improved opt-k-decomp.…”

Section: Related Workmentioning

confidence: 99%

A greedy algorithm for constructing a low-width generalized hypertree decomposition

Katayama

Okawara

Ito

2010

Proceedings of the 13th International Conference on Database Theory

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We propose a greedy algorithm which, given a hypergraph H and a positive integer k, produces a hypertree decomposition of width less than or equal to 3k − 1, or determines that H does not have a generalized hypertree-width less than k. The running time of this algorithm is O(m k+2 n), where m is the number of hyperedges and n is the number of vertices. If k is a constant, it is polynomial. The concepts of (generalized) hypertree decomposition and (generalized) hypertree-width were introduced by Gottlob et al. Many important NP-complete problems in database theory or artificial intelligence are polynomially solvable for classes of instances associated with hypergraphs of bounded hypertree-width. Gottlob et al. also developed a polynomial time algorithm det-k-decomp which, given a hypergraph H and a constant k, computes a hypertree decomposition of width less than or equal to k if the hypertree-width of H is less than or equal to k. The running time of det-k-decomp is O(m 2k n 2 ) in the worst case, where m and n are the number of hyperedges and the number of vertices, respectively. The proposed algorithm is faster than this. The key step of our algorithm is checking whether a set of hyperedges is an obstacle to a hypergraph having low generalized hypertree-width. We call such a local hypergraph structure a k-hyperconnected set. If a hypergraph contains a k-hyperconnected set with a size of at least 2k, it has hypertreewidth of at least k. Adler et al. propose another obstacle called a k-hyperlinked set. We discuss the difference between the two concepts with examples.

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Section: Related Workmentioning

confidence: 99%

A greedy algorithm for constructing a low-width generalized hypertree decomposition

Katayama

Okawara

Ito

2010

Proceedings of the 13th International Conference on Database Theory

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“…However, we note that this is a property of the original input instance, and not of our rule decomposition approach which, in the worst case, will not change the rules in the program at all, and can thus not make things worse. Finally, since lpopt makes use of heuristics to compute tree decompositions (see (Dermaku et al 2008) for details of the heuristics used), some variability in decomposition quality is expected. This can cause variations in grounding time and size for different decompositions of the same rule.…”

Section: Experimental Evaluationmentioning

confidence: 99%

The power of non-ground rules in Answer Set Programming

Bichler¹,

Morak²,

Woltran³

2016

Theory and Practice of Logic Programming

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Answer set programming (ASP) is a well-established logic programming language that offers an intuitive, declarative syntax for problem solving. In its traditional application, a fixed ASP program for a given problem is designed and the actual instance of the problem is fed into the program as a set of facts This approach typically results in programs with comparably short and simple rules However, as is known from complexity analysis, such an approach limits the expressive power of ASP; in fact, an entire NP-check can be encoded into a single large rule body of bounded arity that performs both a guess and a check within the same rule Here, we propose a novel paradigm for encoding hard problems in ASP by making explicit use of large rules which depend on the actual instance of the problem. We illustrate how this new encoding paradigm can be used, providing examples of problems from the first, second, and even third level of the polynomial hierarchy As state-of-the-art solvers are tuned towards short rules, rule decomposition is a key technique in the practical realization of our approach We also provide some preliminary benchmarks which indicate that giving up the convenient way of specifying a fixed program can lead to a significant speed-up. This paper is under consideration for acceptance in TPLP.

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“…In our experiments we have observed that a slightly improved treewidth does not have a significant impact on the efficiency of the dynamic algorithm for our problem domain and therefore we decided to use the three heuristics directly. We initially used an implementation of these heuristics available in a state-of-the-art libraries [21] for tree/hypertree decomposition. Further, we implemented new data structures that store additional information about vertices, their adjacent edges and neighbors to find the next node in the ordering faster.…”

Section: Evaluation Of Tree Decompositions For Aspmentioning

confidence: 99%

Evaluating Tree-Decomposition Based Algorithms for Answer Set Programming

Morak

Musliu

Pichler

et al. 2012

Lecture Notes in Computer Science

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Abstract. A promising approach to tackle intractable problems is given by a combination of decomposition methods with dynamic algorithms. One such decomposition concept is tree decomposition.However, several heuristics for obtaining a tree decomposition exist and, moreover, also the subsequent dynamic algorithm can be laid out differently. In this paper, we provide an experimental evaluation of this combined approach when applied to reasoning problems in propositional answer set programming. More specifically, we analyze the performance of three different heuristics and two different dynamic algorithms, an existing standard version and a novel algorithm based on a more involved data structure, but which provides better theoretical runtime. The results suggest that a suitable combination of the tree decomposition heuristics and the dynamic algorithm has to be chosen carefully. In particular, we observed that the performance of the dynamic algorithm highly depends on certain features (besides treewidth) of the provided tree decomposition. Based on this observation we apply supervised machine learning techniques to automatically select the dynamic algorithm depending on the features of the input tree decomposition.

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Heuristic Methods for Hypertree Decomposition

Cited by 33 publications

References 14 publications

A greedy algorithm for constructing a low-width generalized hypertree decomposition

A greedy algorithm for constructing a low-width generalized hypertree decomposition

The power of non-ground rules in Answer Set Programming

Evaluating Tree-Decomposition Based Algorithms for Answer Set Programming

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