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Approximability of the Minimum Weighted Doubly Resolving Set Problem

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Computing and Combinatorics (COCOON 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8591))

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Abstract

Locating source of diffusion in networks is crucial for controlling and preventing epidemic risks. It has been studied under various probabilistic models. In this paper, we study source location from a deterministic point of view by modeling it as the minimum weighted doubly resolving set problem, which is a strengthening of the well-known metric dimension problem.

Let G be a vertex weighted undirected graph on n vertices. A vertex subset S of G is a doubly resolving set (DRS) of G if for every pair of vertices u,v in G, there exist x,y ∈ S such that the difference of distances (in terms of number of edges) between u and x,y is not equal to the difference of distances between v and x,y. The minimum weighted drs problem consists of finding a DRS in G with minimum total weight. We establish Θ(ln n) approximability of the minimum drs problem on general graphs for both weighted and unweighted versions. This is the first work providing explicit approximation lower and upper bounds for minimum (weighted) drs problem, which are nearly tight. Moreover, we design first known strongly polynomial time algorithms for the minimum weighted drs problem on general wheels and trees with additional constant k ≥ 0 edges.

Research supported in part by NNSF of China under Grant No. 11222109, 11021161 and 10928102, by 973 Project of China under Grant No. 2011CB80800, and by CAS Program for Cross & Cooperative Team of Science & Technology Innovation.

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Authors and Affiliations

  1. Institute of Applied Mathematics, AMSS, Chinese Academy of Sciences, Beijing, 100190, China

    Xujin Chen & Changjun Wang

Authors
  1. Xujin Chen
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  2. Changjun Wang
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Editors and Affiliations

  1. Department of Computer Science, Georgia State University, 34 Peachtree Street, Suite 1410, 30303, Atlanta, GA, USA

    Zhipeng Cai

  2. Department of Computer Science, Georgia State University, 34 Peachtree Street, Suite 1443, 30303, Atlanta, GA, USA

    Alex Zelikovsky

  3. Department of Computer Science, Georgia State University, 34 Peachtree Street, Suite 1449, 30303, Atlanta, GA, USA

    Anu Bourgeois

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Chen, X., Wang, C. (2014). Approximability of the Minimum Weighted Doubly Resolving Set Problem. In: Cai, Z., Zelikovsky, A., Bourgeois, A. (eds) Computing and Combinatorics. COCOON 2014. Lecture Notes in Computer Science, vol 8591. Springer, Cham. https://doi.org/10.1007/978-3-319-08783-2_31

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  • DOI: https://doi.org/10.1007/978-3-319-08783-2_31

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08782-5

  • Online ISBN: 978-3-319-08783-2

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