Abstract
We consider a special set covering problem. This problem is a generalization of finding a minimum clique cover in an interval graph. When formulated as an integer program, the 0-1 constraint matrix of this integer program can be partitioned into an interval matrix and a special 0-1 matrix with a single 1 per column. We show that the value of this formulation is bounded by \( \tfrac{{2k}} {{k + 1}} \) times the value of the LP-relaxation, where k is the maximum row sum of the special matrix. For the “smallest” difficult case, i.e., k = 2, this bound is tight. Also we provide an O(n) 3/2 -approximation algorithm in case k = 2.
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Kovaleva, S., Spieksma, F.C.R. (2001). Approximation of a Geometric Set Covering Problem. In: Eades, P., Takaoka, T. (eds) Algorithms and Computation. ISAAC 2001. Lecture Notes in Computer Science, vol 2223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45678-3_42
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DOI: https://doi.org/10.1007/3-540-45678-3_42
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