An optimal greedy heuristic to color interval graphs
Information Processing Letters
An introduction to parallel algorithms
An introduction to parallel algorithms
Level schedules for mixed-model, Just-in-Time processes
Management Science
Restrictions of graph partition problems. Part I
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
An O(v|v| c |E|) algoithm for finding maximum matching in general graphs
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
Mutual exclusion scheduling with interval graphs or related classes, Part I
Discrete Applied Mathematics
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In this note, the problem of determining disjoint matchings in a set of intervals is investigated (two intervals can be matched if they are disjoint). Such problems find applications in schedules planning. First, we propose a new incremental algorithm to compute maximum disjoint matchings among intervals. We show that this algorithm runs in O(n) time if the intervals are given ordered in input. Additionally, a shorter algorithm is given for the case where the intervals are proper. Then, a NP-complete extension of this problem is considered: the perfect disjoint multidimensional matching problem among intervals. A sufficient condition is established for the existence of such a matching. The proof of this result yields a linear-time algorithm to compute it in this case. Besides, a greedy heuristic is shown to solve the problem in linear time for proper intervals.