Stability number and chromatic number of tolerance graphs
Discrete Applied Mathematics
Complexity and algorithms for reasoning about time: a graph-theoretic approach
Journal of the ACM (JACM)
Proper and unit tolerance graphs
Discrete Applied Mathematics - Special volume: Aridam VI and VII, Rutcor, New Brunswick, NJ, USA (1991 and 1992)
Trapezoid graphs and generalizations, geometry and algorithms
Discrete Applied Mathematics
MAAI '96 Proceedings of symposia in applied mathematics on Mathematical aspects of artificial intelligence
AISMC-1 Proceedings of the International Conference on Artificial Intelligence and Symbolic Mathematical Computation
Algorithms for Weakly Triangulated Graphs
Algorithms for Weakly Triangulated Graphs
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Journal of Graph Theory
Mutual exclusion scheduling with interval graphs or related classes, Part I
Discrete Applied Mathematics
A New Intersection Model and Improved Algorithms for Tolerance Graphs
SIAM Journal on Discrete Mathematics
The Recognition of Tolerance and Bounded Tolerance Graphs
SIAM Journal on Computing
An intersection model for multitolerance graphs: efficient algorithms and hierarchy
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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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.