Annals of Operations Research

, Volume 275, Issue 2, pp 281–295 | Cite as

On interval and circular-arc covering problems

  • Reuven Cohen
  • Mira GonenEmail author
Original Research


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 \(\mathbb {R}\).


Covering Optimization Dynamic programming 



Reuven Cohen thanks the BSF for support. Science and Technology of Israel.


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Authors and Affiliations

  1. 1.Department of MathematicsBar-Ilan UniversityRamat GanIsrael
  2. 2.Department of Computer ScienceAriel UniversityArielIsrael

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