TY - JOUR

T1 - On interval and circular-arc covering problems

AU - Cohen, Reuven

AU - Gonen, Mira

N1 - Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2019/4/15

Y1 - 2019/4/15

N2 - 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.

AB - 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.

KW - Covering

KW - Dynamic programming

KW - Optimization

UR - http://www.scopus.com/inward/record.url?scp=85052636508&partnerID=8YFLogxK

U2 - 10.1007/s10479-018-3025-6

DO - 10.1007/s10479-018-3025-6

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AN - SCOPUS:85052636508

SN - 0254-5330

VL - 275

SP - 281

EP - 295

JO - Annals of Operations Research

JF - Annals of Operations Research

IS - 2

ER -