Abstract
Computing the minimal network (or minimal CSP) representation of a given set of constraints over the Point Algebra (PA) is a fundamental reasoning problem. In this paper we propose a new approach to solving this task which exploits the timegraph representation of a CSP over PA. A timegraph is a graph partitioned into a set of chains on which the search is supported by a metagraph data structure. We introduce a new algorithm that, by making a particular closure of the metagraph, extends the timegraph with information that supports the derivation of the strongest implied constraint between any pair of point variables in constant time. The extended timegraph can be used as a representation of the minimal CSP. We also compare our method and known techniques for computing minimal CSPs over PA. For CSPs that are sparse or exhibit chain structure, our approach has a better worst-case time complexity. Moreover, an experimental analysis indicates that the performance improvements of our approach are practically very significant. This is the case especially for CSPs with a chain structure, but also for randomly generated (both sparse and dense) CSPs.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Delgrande, J., Gupta, A., Van Allen, T.: A comparison of point-based approaches to qualitative temporal reasoning. Artificial Intelligence 131, 135–170 (2001)
Gerevini, A.: Processing qualitative temporal constraints. In: Handbook of Temporal Reasoning in Artificial Intelligence, pp. 247–276. Elsevier, Amsterdam (2005)
Gerevini, A., Schubert, L.: Efficient algorithms for qualitative reasoning about time. Artificial Intelligence 74, 207–248 (1995)
Gerevini, A., Schubert, L.: On computing the minimal labels in time point algebra networks. Computational Intelligence 11(3), 443–448 (1995)
Golumbic, C.M., Shamir, R.: Complexity and algorithms for reasoning about time: a graph-theoretic approach. Journal of the Association for Computing Machinery (ACM) 40(5), 1108–1133 (1993)
van Beek, P.: Reasoning about qualitative temporal information. Artificial Intelligence 58(1-3), 297–321 (1992)
van Beek, P., Cohen, R.: Exact and approximate reasoning about temporal relations. Computational Intelligence 6, 132–144 (1990)
van Beek, P., Manchak, D.W.: The design and experimental analysis of algorithms for temporal reasoning. Journal of Artificial Intelligence Research 4, 1–18 (1996)
Vilain, M., Kautz, H.A.: Constraint propagation algorithms for temporal reasoning. In: Proceedings of the Fifth National Conference of the American Association for Artificial Intelligence (AAAI 1986), pp. 377–382. Morgan Kaufmann, San Francisco (1986)
Vilain, M., Kautz, H.A., van Beek, P.: Constraint propagation algorithms for temporal reasoning: a revised report. In: Weld, D.S, de Kleer, J. (eds.) Readings in Qualitative Reasoning about Physical Systems, pp. 373–381. Morgan Kaufmann, San Mateo, CA (1990)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gerevini, A., Saetti, A. (2007). Efficient Computation of Minimal Point Algebra Constraints by Metagraph Closure. In: Bessière, C. (eds) Principles and Practice of Constraint Programming – CP 2007. CP 2007. Lecture Notes in Computer Science, vol 4741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74970-7_23
Download citation
DOI: https://doi.org/10.1007/978-3-540-74970-7_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74969-1
Online ISBN: 978-3-540-74970-7
eBook Packages: Computer ScienceComputer Science (R0)