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http://dx.doi.org/10.6109/jkiice.2022.26.10.1531

Minimizing the Maximum Weighted Membership of Interval Cover of Points  

Kim, Jae-Hoon (Department of Computer Engineering, Busan University of Foreign Studies)
Publication Information
Journal of the Korea Institute of Information and Communication Engineering / v.26, no.10, 2022 , pp. 1531-1536 More about this Journal
Abstract
This paper considers a problem to find a set of intervals containing all the points for the given n points and m intervals on a line, This is a special case of the set cover problem, well known as an NP-hard problem. As optimization criteria of the problem, there are minimizing the number of intervals to cover the points, maximizing the number of points each of which is covered by exactly one interval, and so on. In this paper, the intervals have weights and the sum of weights of intervals to cover a point is defined as a membership of the point. We will study the problem to find an interval cover minimizing the maximum of memberships of points. Using the dynamic programming method, we provide an O(m2)-time algorithm to improve the time complexity O(nm log n) given in the previous work.
Keywords
interval cover; set cover; optimization; membership; dynamic programming;
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