Maximum Red/Blue Interval Matching with Applications

Authors:
Danny Z. Chen;Xiaobo Hu;Xiaodong Wu
Affiliations:
-;-;-
Venue:
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
Year:
2001

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Abstract

In this paper, we consider the problem of computing a maximum cardinality matching among a set I of n intervals that are colored as either red or blue, such that a pair of intervals in I can be matched only if they overlap with each other and have different colors. This problem arises in some applications such as radiosurgery treatment planning. We present a greedy algorithm for this problem that runs in O(n log log n) time for sorted input.We also solve a useful generalization of this red/blue interval matching problem in the same time bound.