Abstract
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.
The author works under contract with the firm Prologia-Groupe Air Liquide.
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Gardi, F. (2003). Efficient Algorithms for Disjoint Matchings among Intervals and Related Problems. In: Calude, C.S., Dinneen, M.J., Vajnovszki, V. (eds) Discrete Mathematics and Theoretical Computer Science. DMTCS 2003. Lecture Notes in Computer Science, vol 2731. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45066-1_13
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DOI: https://doi.org/10.1007/3-540-45066-1_13
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