Abstract
Symmetry has been studied in both propositional calculus and discrete constraint satisfaction problems. This has been shown to reduce considerably the search space. In this paper, we extend the study to qualitative interval networks. We provide experimental tests on the performances of a variant of Ladkin and Reinefeld's search algorithm in the following two cases: (1) the algorithm as provided by its authors, with no advantage of symmetry, and (2) the algorithm to which is added symmetry detection during the search. The experiments show that symmetries are profitable for hard problems.
Preview
Unable to display preview. Download preview PDF.
References
J F Allen. Maintaining knowledge about temporal intervals. Communications of the Association for Computing Machinery, 26(11):832–843, 1983.
B Benhamou. Study of symmetry in constraint satisfaction problems. In Proceedings PPCP, 1994.
B Benhamou and L Sais. Tractability through symmetries in propositional calculus. Automated Reasoning, 12:89–102, 1994.
S Benzer. On the topology of the genetic fine structure. Proceedings Nat. Acad. Sci., USA 45:1607–1620, 1959.
E C Freuder. Synthesizing constraint expressions. Communications of the Association for Computing Machinery, 21:958–966, 1978.
E C Freuder. A sufficient condition for backtrack-free search. Journal of the Association for Computing Machinery, 29:24–32, 1982.
E C Freuder. Eliminating interchangeable values in constraint satisfaction problems. In Proceedings of the AAAI-91, pages 227–233, Anaheim, CA, 1991. AAAI Press/The MIT Press.
J Gasching. Experimental case studies of backtrack vs. waltz-type vs. new algorithms for satisfying assignment problems. In Proceedings of the Second Biennial Conference of the Canadian Society for Computational Studies of Intelligence, pages 268–277, Toronto, Ont., 1978.
M C Golumbic and R Shamir. Complexity and algorithms for reasoning about time: a graph-theoretic approach. Journal of the Association for Computing Machinery, 40(5):1108–1133, 1993.
R M Haralick and G L Elliott. Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence, 14:263–313, 1980.
A Haselbök. Exploiting interchangeabilities in constraint satisfaction problems. In Proceedings of the IJCAI-93, pages 282–287, Chambéry, France, 1993.
A Isli and H Bennaceur. Qualitative interval networks: combining path consistency and circuit consistency in the search for a solution. In Proceedings of the International Workshop of Temporal Representation and Reasoning (TIME-96), Key West, Florida, 1996.
P Ladkin and A Reinefeld. Effective solution of qualitative constraint problems. Artificial Intelligence, 57:105–124, 1992.
A K Mackworth. Consistency in networks of relations. Artificial Intelligence, 8:99–118, 1977.
U Montanari. Networks of constraints: Fundamental properties and applications to picture processing. Information Sciences, 7:95–132, 1974.
B Nebel. Solving hard qualitative temporal reasoning problems: Evaluating the efficiency of using the ord-horn class. CONSTRAINTS, 1(3):175–190, 1997.
G S Tseitin. On the complexity of derivation in propositional calculus. In Structures in the constructive Mathematics and Mathematical logic, pages 115–125. Shsenko, H A O, 1968.
R E Valdés-Pérez. The satisfiability of temporal constraint networks. In Proceedings of the AAAI-87, pages 256–260, Seattle, WA, 1987.
P van Beek. Reasoning about qualitative temporal information. Artificial Intelligence, 58:297–326, 1992.
P van Beek and D M Manchak. The design and experimental analysis of algorithms for temporal reasoning. Journal of Artificial Intelligence Research, 4:1–18, 1996.
M B Vilain and H Kautz. Constraint propagation algorithms for temporal reasoning. In Proceedings AAAI-86, Philadelphia, August 1986.
M B Vilain, H Kautz, and P van Beek. Constraint propagation algorithms for temporal reasoning: A revised report. In Morgan Kaufmann, editor, Readings in Qualitative Reasoning about Physical Systems, pages 373–381, San Mateo, CA, 1990. Revised version of paper that appeared in Proceedings of AAAI-86, 377–382.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Benhamou, B., Isli, A. (1998). Study of symmetry in qualitative temporal interval networks. In: Giunchiglia, F. (eds) Artificial Intelligence: Methodology, Systems, and Applications. AIMSA 1998. Lecture Notes in Computer Science, vol 1480. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0057437
Download citation
DOI: https://doi.org/10.1007/BFb0057437
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64993-9
Online ISBN: 978-3-540-49793-6
eBook Packages: Springer Book Archive