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Deterministic Sampling Algorithms for Network Design

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Abstract

For several NP-hard network design problems, the best known approximation algorithms are remarkably simple randomized algorithms called Sample-Augment algorithms in Gupta et al. (J. ACM 54(3):11, 2007). The algorithms draw a random sample from the input, solve a certain subproblem on the random sample, and augment the solution for the subproblem to a solution for the original problem. We give a general framework that allows us to derandomize most Sample-Augment algorithms, i.e. to specify a specific sample for which the cost of the solution created by the Sample-Augment algorithm is at most a constant factor away from optimal. Our approach allows us to give deterministic versions of the Sample-Augment algorithms for the connected facility location problem, in which the open facilities need to be connected by either a tree or a tour, the virtual private network design problem, 2-stage rooted stochastic Steiner tree problem with independent decisions, the a priori traveling salesman problem and the single sink buy-at-bulk problem. This partially answers an open question posed in Gupta et al. (J. ACM 54(3):11, 2007).

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Article Open access 03 October 2017

L.-C. Zhang & M. Patone

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Authors and Affiliations

  1. Institute for Theoretical Computer Science, Tsinghua University, Beijing, 100084, P.R. China

    Anke van Zuylen

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  1. Anke van Zuylen
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Correspondence to Anke van Zuylen.

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A preliminary version of this paper [28] appeared in the Proceedings of the 16th European Symposium on Algorithms, 2008.

This research was conducted while the author was at Cornell University and was supported in part by NSF grant CCF-0514628, the National Natural Science Foundation of China Grant 60553001, and the National Basic Research Program of China Grant 2007CB807900,2007CB807901.

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van Zuylen, A. Deterministic Sampling Algorithms for Network Design. Algorithmica 60, 110–151 (2011). https://doi.org/10.1007/s00453-009-9344-x

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