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Encyclopedia of Algorithms pp 1331–1334Cite as

Min-Sum Set Cover and Its Generalizations

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Years and Authors of Summarized Original Work

  • 2004; Feige, Lovász, Tetali

  • 2010; Bansal, Gupta, Krishnaswamy

  • 2011; Azar, Gamzu

Problem Definition

The min sum set cover (MSSC) problem is a latency version of the set cover problem. The input to MSSC consists of a collection of sets \(\{S_{i}\}_{i\in [m]}\) over a universe of elements [n] : = { 1, 2, 3, …, n}. The goal is to schedule elements, one at a time, to hit all sets as early on average as possible. Formally, we would like to find a permutation \(\pi : [n] \rightarrow [n]\) of the elements [n] (π(i) is the ith element in the ordering) such that the average (or equivalently total) cover time of the sets \(\{S_{i}\}_{i\in [m]}\) is minimized. The cover time of a set S i is defined as the earliest time t such that π(t) ∈ S i . For convenience, we will say that we schedule/process element π(i) at time i.

Since MSSC was introduced in [4], several generalizations have been studied. Here we discuss two of them. In the generalized min sum...

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Recommended Reading

  1. Azar Y, Gamzu I (2011) Ranking with submodular valuations. In: SODA, San Francisco, pp 1070–1079

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  2. Azar Y, Gamzu I, Yin X (2009) Multiple intents re-ranking. In: STOC, Bethesda, pp 669–678

    MATH  Google Scholar 

  3. Bansal N, Gupta A, Krishnaswamy R (2010) A constant factor approximation algorithm for generalized min-sum set cover. In: SODA, Austin, pp 1539–1545

    MATH  Google Scholar 

  4. Feige U, Lovász L, Tetali P (2004) Approximating min sum set cover. Algorithmica 40(4):219–234

    Article  MathSciNet  MATH  Google Scholar 

  5. Im S, Nagarajan V, van der Zwaan R (2012) Minimum latency submodular cover. In: ICALP (1), Warwick, pp 485–497

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  6. Im S, Sviridenko M, Zwaan R (2014) Preemptive and non-preemptive generalized min sum set cover. Math Program 145(1–2):377–401

    MathSciNet  MATH  Google Scholar 

  7. Skutella M, Williamson DP (2011) A note on the generalized min-sum set cover problem. Oper Res Lett 39(6):433–436

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Electrical Engineering and Computer Sciences (EECS), University of California, Merced, CA, USA

    Sungjin Im

Authors
  1. Sungjin Im
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Corresponding author

Correspondence to Sungjin Im .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Im, S. (2016). Min-Sum Set Cover and Its Generalizations. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_806

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