Coloring algorithms for tolerance graphs: Reasoning and scheduling with interval constraints

Martin Charles Golumbic; Assaf Siani

doi:10.1007/3-540-45470-5

Coloring algorithms for tolerance graphs: Reasoning and scheduling with interval constraints

Martin Charles Golumbic, Assaf Siani

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Interval relations play a significant role in constraint-based temporal reasoning, resource allocation and scheduling problems. For example, the intervals may represent events in time which may conflict or may be compatible, or they may represent tasks to be performed according to a timetable which must be assigned distinct resources like processors or people. In previous work [G93, GS93, G98], we explored the interaction between the interval algebras studied in artificial intelligence and the interval graphs and orders studied in combinatorial mathematics, extending results in both disciplines. In this paper, we investigate algorithmic problems on tolerance graphs, a family which generalizes interval graphs, and which therefore have broader application. Tolerance graph models can represent qualitative and quantitative relations in situations where the intervals can tolerate a certain degree of overlap without being in conflict. We present a coloring algorithm for a tolerance graph on n vertices whose running time is O(n²), given the tolerance representation, thus improving previously known results. The coloring problem on intervals has direct application to resource allocation and scheduling temporal processes.

Original language	English
Title of host publication	Artificial Intelligence, Automated Reasoning and Symbolic Computation - Joint International Conferences AISC 2002 and Calculemus 2002, Proceedings
Editors	Laurent Henocque, Jacques Calmet, Belaid Benhamou, Olga Caprotti, Volker Sorge
Publisher	Springer Verlag
Pages	196-207
Number of pages	12
ISBN (Print)	3540438653, 9783540438656
DOIs	https://doi.org/10.1007/3-540-45470-5
State	Published - 2002
Event	Joint Conferences on 6th Artificial Intelligence and Symbolic Computation, AISC 2002 and 10th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2002 - Marseille, France Duration: 1 Jul 2002 → 5 Jul 2002

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2385
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	Joint Conferences on 6th Artificial Intelligence and Symbolic Computation, AISC 2002 and 10th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2002
Country/Territory	France
City	Marseille
Period	1/07/02 → 5/07/02

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2002.

Keywords

AI
Coloring tolerance graphs
OR applications
Reasoning

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/3-540-45470-5

Cite this

Golumbic, M. C., & Siani, A. (2002). Coloring algorithms for tolerance graphs: Reasoning and scheduling with interval constraints. In L. Henocque, J. Calmet, B. Benhamou, O. Caprotti, & V. Sorge (Eds.), Artificial Intelligence, Automated Reasoning and Symbolic Computation - Joint International Conferences AISC 2002 and Calculemus 2002, Proceedings (pp. 196-207). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2385). Springer Verlag. https://doi.org/10.1007/3-540-45470-5

Golumbic, Martin Charles ; Siani, Assaf. / Coloring algorithms for tolerance graphs : Reasoning and scheduling with interval constraints. Artificial Intelligence, Automated Reasoning and Symbolic Computation - Joint International Conferences AISC 2002 and Calculemus 2002, Proceedings. editor / Laurent Henocque ; Jacques Calmet ; Belaid Benhamou ; Olga Caprotti ; Volker Sorge. Springer Verlag, 2002. pp. 196-207 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Golumbic, MC & Siani, A 2002, Coloring algorithms for tolerance graphs: Reasoning and scheduling with interval constraints. in L Henocque, J Calmet, B Benhamou, O Caprotti & V Sorge (eds), Artificial Intelligence, Automated Reasoning and Symbolic Computation - Joint International Conferences AISC 2002 and Calculemus 2002, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2385, Springer Verlag, pp. 196-207, Joint Conferences on 6th Artificial Intelligence and Symbolic Computation, AISC 2002 and 10th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2002, Marseille, France, 1/07/02. https://doi.org/10.1007/3-540-45470-5

Coloring algorithms for tolerance graphs: Reasoning and scheduling with interval constraints. / Golumbic, Martin Charles; Siani, Assaf.
Artificial Intelligence, Automated Reasoning and Symbolic Computation - Joint International Conferences AISC 2002 and Calculemus 2002, Proceedings. ed. / Laurent Henocque; Jacques Calmet; Belaid Benhamou; Olga Caprotti; Volker Sorge. Springer Verlag, 2002. p. 196-207 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2385).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - Interval relations play a significant role in constraint-based temporal reasoning, resource allocation and scheduling problems. For example, the intervals may represent events in time which may conflict or may be compatible, or they may represent tasks to be performed according to a timetable which must be assigned distinct resources like processors or people. In previous work [G93, GS93, G98], we explored the interaction between the interval algebras studied in artificial intelligence and the interval graphs and orders studied in combinatorial mathematics, extending results in both disciplines. In this paper, we investigate algorithmic problems on tolerance graphs, a family which generalizes interval graphs, and which therefore have broader application. Tolerance graph models can represent qualitative and quantitative relations in situations where the intervals can tolerate a certain degree of overlap without being in conflict. We present a coloring algorithm for a tolerance graph on n vertices whose running time is O(n2), given the tolerance representation, thus improving previously known results. The coloring problem on intervals has direct application to resource allocation and scheduling temporal processes.

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SN - 9783540438656

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Golumbic MC, Siani A. Coloring algorithms for tolerance graphs: Reasoning and scheduling with interval constraints. In Henocque L, Calmet J, Benhamou B, Caprotti O, Sorge V, editors, Artificial Intelligence, Automated Reasoning and Symbolic Computation - Joint International Conferences AISC 2002 and Calculemus 2002, Proceedings. Springer Verlag. 2002. p. 196-207. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-45470-5

Coloring algorithms for tolerance graphs: Reasoning and scheduling with interval constraints

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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