On interval and circular-arc covering problems

Reuven Cohen, Mira Gonen

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1 Scopus citations


In this paper we study several related problems of finding optimal interval and circular-arc covering. We present solutions to the maximum k-interval (k-circular-arc) coverage problems, in which we want to cover maximum weight by selecting k intervals (circular-arcs) out of a given set of intervals (circular-arcs), respectively, the weighted interval covering problem, in which we want to cover maximum weight by placing k intervals with a given length, and the k-centers problem. The general sets version of the discussed problems, namely the general measure k-centers problem and the maximum covering problem for sets are known to be NP-hard. However, for the one dimensional restrictions studied here, and even for circular-arc graphs, we present efficient, polynomial time, algorithms that solve these problems. Our results for the maximum k-interval and k-circular-arc covering problems hold for any right continuous positive measure on R.

Original languageEnglish
Pages (from-to)281-295
Number of pages15
JournalAnnals of Operations Research
Issue number2
StatePublished - 15 Apr 2019


  • Covering
  • Dynamic programming
  • Optimization


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