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Vertex Fault-Tolerant Spanners for Weighted Points in Polygonal Domains

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Combinatorial Optimization and Applications (COCOA 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12577))

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Abstract

Given a set S of n points, a weight function w to associate a non-negative weight to each point in S, a positive integer \(k \ge 1\), and a real number \(\epsilon > 0\), we devise the following algorithms to compute a k-vertex fault-tolerant spanner network G(S, E) for the metric space induced by the weighted points in S: (1) When the points in S are located in a simple polygon, we present an algorithm to compute G with multiplicative stretch \(\sqrt{10}+\epsilon \), and the number of edges in G is \(O(k n (\lg {n})^2)\). (2) When the points in S are located in the free space of a polygonal domain \(\mathcal{P}\), we present an algorithm to compute G of size \(O(\sqrt{h} k n(\lg {n})^2)\) and its multiplicative stretch is \(6+\epsilon \). Here, h is the number of simple polygonal holes in \(\mathcal{P}\).

This research is supported in part by SERB MATRICS grant MTR/2017/000474.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, IIT Guwahati, Guwahati, India

    R. Inkulu & Apurv Singh

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  1. R. Inkulu
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  2. Apurv Singh
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Correspondence to R. Inkulu .

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Editors and Affiliations

  1. The University of Texas at Dallas, Richardson, TX, USA

    Weili Wu

  2. Xiamen University, Xiamen, China

    Zhongnan Zhang

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Inkulu, R., Singh, A. (2020). Vertex Fault-Tolerant Spanners for Weighted Points in Polygonal Domains. In: Wu, W., Zhang, Z. (eds) Combinatorial Optimization and Applications. COCOA 2020. Lecture Notes in Computer Science(), vol 12577. Springer, Cham. https://doi.org/10.1007/978-3-030-64843-5_32

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  • DOI: https://doi.org/10.1007/978-3-030-64843-5_32

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