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On Column-Restricted and Priority Covering Integer Programs

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Integer Programming and Combinatorial Optimization (IPCO 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6080))

Abstract

In a column-restricted covering integer program (CCIP), all the non-zero entries of any column of the constraint matrix are equal. Such programs capture capacitated versions of covering problems. In this paper, we study the approximability of CCIPs, in particular, their relation to the integrality gaps of the underlying 0,1-CIP.

If the underlying 0,1-CIP has an integrality gap O(γ), and assuming that the integrality gap of the priority version of the 0,1-CIP is O(ω), we give a factor O(γ + ω) approximation algorithm for the CCIP. Priority versions of 0,1-CIPs (PCIPs) naturally capture quality of service type constraints in a covering problem.

We investigate priority versions of the line (PLC) and the (rooted) tree cover (PTC) problems. Apart from being natural objects to study, these problems fall in a class of fundamental geometric covering problems. We bound the integrality of certain classes of this PCIP by a constant. Algorithmically, we give a polytime exact algorithm for PLC, show that the PTC problem is APX-hard, and give a factor 2-approximation algorithm for it.

Supported by NSERC grant no. 288340 and by an Early Research Award.

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Author information

Authors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, Canada, N2L 3G1

    Deeparnab Chakrabarty, Elyot Grant & Jochen Könemann

Authors
  1. Deeparnab Chakrabarty
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  2. Elyot Grant
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  3. Jochen Könemann
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Editor information

Editors and Affiliations

  1. Institute of Mathematics, École Polytechnique Féderale de Lausanne, 1015, Lausanne, Switzerland

    Friedrich Eisenbrand

  2. McGill University, 805 Sherbrooke West, H3A 2K6, Montreal, Quebec, Canada

    F. Bruce Shepherd

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Chakrabarty, D., Grant, E., Könemann, J. (2010). On Column-Restricted and Priority Covering Integer Programs. In: Eisenbrand, F., Shepherd, F.B. (eds) Integer Programming and Combinatorial Optimization. IPCO 2010. Lecture Notes in Computer Science, vol 6080. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13036-6_27

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  • DOI: https://doi.org/10.1007/978-3-642-13036-6_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13035-9

  • Online ISBN: 978-3-642-13036-6

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