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Proceedings Article, Paper


@InProceedings
Beitrag in Tagungsband, Workshop
Author, Editor
Author(s):
Hoffmann, Jörg
Gomes, Carla
Selman, Bart		dblp
dblp
dblp
Not MPG Author(s):
Gomes, Carla
Selman, Bart
Editor(s):
Long, Derek
Smith, Stephen F.
Borrajo, Daniel
McCluskey, Lee		dblp
dblp
dblp
dblp
Not MPII Editor(s):
Long, Derek
Smith, Stephen F.
Borrajo, Daniel
McCluskey, Lee
BibTeX cite key*:
HoffmannEtal2006a
Title, Booktitle
Title*:
Structure and Problem Hardness: Goal Asymmetry and DPLL Proofs in SAT-Based Planning
Booktitle*:
Proceedings of the Sixteenth International Conference on Automated Planning and Scheduling (ICAPS 2006)
Event, URLs
Conference URL::
http://icaps06.icaps-conference.org/
Downloading URL:
Event Address*:
The English Lake District
Language:
English
Event Date*
(no longer used):
Organization:
Event Start Date:
6 June 2006
Event End Date:
10 June 2006
Publisher
Name*:
AAAI
URL:
http://www.aaai.org/
Address*:
Menlo Park, USA
Type:
Vol, No, Year, pp.
Series:
Volume:
Number:
Month:
Pages:
284-293
Year*:
2006
VG Wort Pages:
ISBN/ISSN:
978-1-57735-270-9
Sequence Number:
DOI:
Note, Abstract, ©
(LaTeX) Abstract:
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.
URL for the Abstract:
http://www.aaai.org/Library/ICAPS/2006/icaps06-029.php
Download
Access Level:
Public

Correlation
MPG Unit:
Max-Planck-Institut für Informatik
MPG Subunit:
Programming Logics Group
Appearance:
MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat, CCL bibliography, VG Wort



BibTeX Entry:
@INPROCEEDINGS{HoffmannEtal2006a,
AUTHOR = {Hoffmann, J{\"o}rg and Gomes, Carla and Selman, Bart},
 EDITOR = {Long, Derek and Smith, Stephen F. and Borrajo, Daniel and McCluskey, Lee},
 TITLE = {Structure and Problem Hardness: Goal Asymmetry and DPLL Proofs in SAT-Based Planning},
 BOOKTITLE = {Proceedings of the Sixteenth International Conference on Automated Planning and Scheduling (ICAPS 2006)},
 PUBLISHER = {AAAI},
 YEAR = {2006},
 PAGES = {284--293},
 ADDRESS = {The English Lake District},
 ISBN = {978-1-57735-270-9},
}

Entry last modified by Uwe Brahm, 01/28/2008
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Editor(s)
Jörg Hoffmann		Created
02/13/2006 11:36:23 AM
Revisions
2.
1.
0.

Editor(s)
Uwe Brahm
Uwe Brahm
Jörg Hoffmann

Edit Dates
2007-04-24 18:10:55
2007-04-24 18:01:51
02/13/2006 11:36:23 AM