Abstract
The input to the min sum set cover problem is a collection of n sets that jointly cover m elements. The output is a linear order on the sets, namely, in every time step from 1 to n exactly one set is chosen. For every element, this induces a first time step by which it is covered. The objective is to find a linear arrangement of the sets that minimizes the sum of these first time steps over all elements.
We show that a greedy algorithm approximates min sum set cover within a ratio of 4. This result was implicit in work of Bar-Noy, Bellare, Halldorsson, Shachnai and Tamir (1998) on chromatic sums, but we present a simpler proof. We also show that for every ∈ > 0, achieving an approximation ratio of 4 - ∈ is NP-hard. For the min sum vertex cover version of the problem, we show that it can be approximated within a ratio of 2, and is NP-hard to approximate within some constant ρ > 1.
research in part supported by the NSF grant DMS-0100298
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© 2002 Springer-Verlag Berlin Heidelberg
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Feige, U., Lovász, L., Tetali, P. (2002). Approximating Min-sum Set Cover. In: Jansen, K., Leonardi, S., Vazirani, V. (eds) Approximation Algorithms for Combinatorial Optimization. APPROX 2002. Lecture Notes in Computer Science, vol 2462. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45753-4_10
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DOI: https://doi.org/10.1007/3-540-45753-4_10
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