The Impact of Treewidth on Grounding and Solving of Answer Set Programs

In this paper, we aim to study how the performance of modern answer set programming (ASP) solvers is influenced by the treewidth of the input program and to investigate the consequences of this relationship. We first perform an experimental evaluation that shows that the solving performance is heavi...

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Bibliographic Details
Published in:The Journal of artificial intelligence research Vol. 67; pp. 35 - 80
Main Authors: Bliem, Bernhard, Morak, Michael, Moldovan, Marius, Woltran, Stefan
Format: Journal Article
Language:English
Published: San Francisco AI Access Foundation 01.01.2020
Subjects:
Artificial intelligence
Complexity
Declarative programming
Mathematical programming
ISSN:1076-9757, 1076-9757, 1943-5037
Online Access:Get full text
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Summary:In this paper, we aim to study how the performance of modern answer set programming (ASP) solvers is influenced by the treewidth of the input program and to investigate the consequences of this relationship. We first perform an experimental evaluation that shows that the solving performance is heavily influenced by treewidth, given ground input programs that are otherwise uniform, both in size and construction. This observation leads to an important question for ASP, namely, how to design encodings such that the treewidth of the resulting ground program remains small. To this end, we study two classes of disjunctive programs, namely guarded and connection-guarded programs. In order to investigate these classes, we formalize the grounding process using MSO transductions. Our main results show that both classes guarantee that the treewidth of the program after grounding only depends on the treewidth (and the maximum degree, in case of connection-guarded programs) of the input instance. In terms of parameterized complexity, our findings yield corresponding FPT results for answer-set existence for bounded treewidth (and also degree, for connection-guarded programs) of the input instance. We further show that bounding treewidth alone leads to NP-hardness in the data complexity for connection-guarded programs, which indicates that the two classes are fundamentally different. Finally, we show that for both classes, the data complexity remains as hard as in the general case of ASP.
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ISSN:1076-9757
1076-9757
1943-5037
DOI:10.1613/jair.1.11515