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  Structure and Problem Hardness: Goal Asymmetry and DPLL Proofs in SAT-Based Planning

Hoffmann, J., Gomes, C., & Selman, B. (2006). Structure and Problem Hardness: Goal Asymmetry and DPLL Proofs in SAT-Based Planning. In Proceedings of the Sixteenth International Conference on Automated Planning and Scheduling (ICAPS 2006) (pp. 284-293). Menlo Park, USA: AAAI.

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 Urheber:
Hoffmann, Jörg1, Autor           
Gomes, Carla, Autor
Selman, Bart, Autor
Long, Derek, Herausgeber
Smith, Stephen F., Herausgeber
Borrajo, Daniel, Herausgeber
McCluskey, Lee, Herausgeber
Affiliations:
1Programming Logics, MPI for Informatics, Max Planck Society, ou_40045              

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Schlagwörter: -
 Zusammenfassung: In AI Planning, as well as Verification, a successful method is to compile the application into boolean satisfiability (SAT), and solve it with state-of-the-art DPLL-based procedures. There is a lack of formal understanding why this works so well. Focussing on the Planning context, we identify a form of problem structure concerned with the symmetrical or asymmetrical nature of the cost of achieving the individual planning goals. We quantify this sort of structure with a simple numeric parameter called AsymRatio, ranging between 0 and 1. We show empirically that AsymRatio correlates strongly with SAT solver performance in a broad range of Planning benchmarks, including the domains used in the 3rd International Planning Competition. We then examine carefully crafted synthetic planning domains that allow to control the amount of structure, and that are clean enough for a rigorous analysis of the combinatorial search space. The domains are parameterized by size n, and by a structure parameter k, so that AsymRatio is asymptotic to k/n. The CNFs we examine are unsatisfiable, encoding one planning step less than the length of the optimal plan. We prove upper and lower bounds on the size of the best possible DPLL refutations, under different settings of k, as a function of n. We also identify the best possible sets of branching variables (backdoors). With minimum AsymRatio, we prove exponential lower bounds, and identify minimal backdoors of size linear in the number of variables. With maximum AsymRatio, we identify logarithmic DPLL refutations (and backdoors), showing a doubly exponential gap between the two structural extreme cases. This provides a concrete insight into the practical efficiency of modern SAT solvers.

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Sprache(n): eng - English
 Datum: 2007-04-242006
 Publikationsstatus: Erschienen
 Seiten: -
 Ort, Verlag, Ausgabe: Menlo Park, USA : AAAI
 Inhaltsverzeichnis: -
 Art der Begutachtung: -
 Identifikatoren: eDoc: 314640
Anderer: Local-ID: C1256104005ECAFC-216DB24E61769B54C1257114003A4349-HoffmannEtal2006a
 Art des Abschluß: -

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Titel: Untitled Event
Veranstaltungsort: The English Lake District
Start-/Enddatum: 2006-06-06

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Titel: Proceedings of the Sixteenth International Conference on Automated Planning and Scheduling (ICAPS 2006)
Genre der Quelle: Konferenzband
 Urheber:
Affiliations:
Ort, Verlag, Ausgabe: Menlo Park, USA : AAAI
Seiten: - Band / Heft: - Artikelnummer: - Start- / Endseite: 284 - 293 Identifikator: ISBN: 978-1-57735-270-9