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Approximation Algorithms for Prize-Collecting Network Design Problems with General Connectivity Requirements

  • Chandrashekhar Nagarajan
  • Yogeshwer Sharma
  • David P. Williamson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5426)

Abstract

In this paper, we introduce the study of prize-collecting network design problems having general connectivity requirements. Prior work considered only 0-1 or very limited connectivity requirements. We introduce general connectivity requirements in the prize-collecting generalized Steiner tree framework of Hajiaghayi and Jain [9], and consider penalty functions linear in the violation of the connectivity requirements. Using Jain’s iterated rounding algorithm [11] as a black box, and ideas from Goemans [7] and Levi, Lodi, Sviridenko [14], we give a 2.54-factor approximation algorithm for the problem. We also generalize the 0-1 requirements of PCF problem introduced by Sharma, Swamy, and Williamson [15] to include general connectivity requirements. Here we assume that the monotone submodular penalty function of Sharma et al. is generalized to a multiset function that can be decomposed into functions in the same form as that of Sharma et al. Using ideas from Goemans and Berstimas [6], we give an (αlogK)-approximation algorithm for the resulting problem, where K is the maximum connectivity requirement, and α= 2.54.

Keywords

Approximation Algorithm Penalty Function Travel Salesman Problem Steiner Tree Network Design Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Chandrashekhar Nagarajan
    • 1
  • Yogeshwer Sharma
    • 2
  • David P. Williamson
    • 1
  1. 1.School of OR&IECornell UniversityIthacaUSA
  2. 2.Department of Computer ScienceCornell UniversityIthacaUSA

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