An O(n1.5) algorithm to color proper circular arcs
Discrete Applied Mathematics
NP-completeness of graph decomposition problems
Journal of Complexity
Scheduling with constrained processor allocation for interval orders
Computers and Operations Research
Simple linear time recognition of unit interval graphs
Information Processing Letters
Restrictions of graph partition problems. Part I
Theoretical Computer Science
Circular convex bipartite graphs: maximum matching and Hamiltonian circuits
Information Processing Letters
A Linear Algorithm for Maximum Weight Cliques in ProperCircular Arc Graphs
SIAM Journal on Discrete Mathematics
Theoretical Computer Science
Restricted coloring models for timetabling
Proceedings of an international symposium on Graphs and combinatorics
Matching and multidimensional matching in chordal and strongly chordal graphs
Discrete Applied Mathematics
Bounded vertex coloring of trees
Discrete Mathematics
Scheduling Computer and Manufacturing Processes
Scheduling Computer and Manufacturing Processes
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Linear-Time Representation Algorithms for Proper Circular-Arc Graphs and Proper Interval Graphs
SIAM Journal on Computing
On Complexity of Some Chain and Antichain Partition Problems
WG '91 Proceedings of the 17th International Workshop
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
Coloring Algorithms for Tolerance Graphs: Reasoning and Scheduling with Interval Constraints
AISC '02/Calculemus '02 Proceedings of the Joint International Conferences on Artificial Intelligence, Automated Reasoning, and Symbolic Computation
The mutual exclusion scheduling problem for permutation and comparability graphs
Information and Computation
An Optimal Solution for the Channel-Assignment Problem
IEEE Transactions on Computers
Mutual exclusion scheduling with interval graphs or related classes. Part II
Discrete Applied Mathematics
Efficient algorithms for disjoint matchings among intervals and related problems
DMTCS'03 Proceedings of the 4th international conference on Discrete mathematics and theoretical computer science
Mutual exclusion scheduling with interval graphs or related classes. Part II
Discrete Applied Mathematics
Discrete Applied Mathematics
Scheduling jobs on identical machines with agreement graph
Computers and Operations Research
Bin Packing with Conflicts: A Generic Branch-and-Price Algorithm
INFORMS Journal on Computing
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In this paper, the mutual exclusion scheduling problem is addressed. Given a simple and undirected graph G and an integer k, the problem is to find a minimum coloring of G such that each color is used at most k times. When restricted to interval graphs or related classes like circular-arc graphs and tolerance graphs, the problem has some applications in workforce planning. Unfortunately, the problem is shown to be NP-hard for interval graphs, even if k is a constant greater than or equal to four [H.L. Bodlaender and K. Jansen Restrictions of graph partition problems. Part I, Theoretical Computer Science 148(1995) pp. 93-109]. Several polynomial-time solvable cases significant in practice are exhibited here, for which we took care to devise simple and efficient algorithms (in particular linear-time and space algorithms). On the other hand, by reinforcing the NP-hardness result of Bodlaender and Jansen, we obtain a more precise cartography of the complexity of the problem for the classes of graphs studied.