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Geodesic Fault-Tolerant Additive Weighted Spanners

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Computing and Combinatorics (COCOON 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11653))

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Abstract

Let S be a set of n points and let w be a function that assigns non-negative weights to points in S. The additive weighted distance \(d_w(p, q)\) between two points \(p,q \in S\) is defined as \(w(p) + d(p, q) + w(q)\) if \(p \ne q\) and it is zero if \(p = q\). Here, d(p, q) is the geodesic Euclidean distance between p and q. For a real number \(t > 1\), a graph G(S, E) is called a t-spanner for the weighted set S of points if for any two points p and q in S the distance between p and q in graph G is at most t.\(d_w(p, q)\) for a real number \(t > 1\). For some integer \(k \ge 1\), a t-spanner G for the set S is a (k, t)-vertex fault-tolerant additive weighted spanner, denoted with (k, t)-VFTAWS, if for any set \(S' \subset S\) with cardinality at most k, the graph \(G \setminus S'\) is a t-spanner for the points in \(S \setminus S'\). For any given real number \(\epsilon > 0\), we present algorithms to compute a \((k, 4+\epsilon )\)-VFTAWS for the metric space \((S, d_w)\) resulting from the following: (i) points in S are in the free space of the polygonal domain, (ii) points in S lying on a terrain.

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

    Sukanya Bhattacharjee & R. Inkulu

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  1. Sukanya Bhattacharjee
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  2. R. Inkulu
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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

    Ding-Zhu Du

  2. Xidian University, Xi'an, China

    Zhenhua Duan

  3. Xidian University, Xi'an, China

    Cong Tian

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Bhattacharjee, S., Inkulu, R. (2019). Geodesic Fault-Tolerant Additive Weighted Spanners. In: Du, DZ., Duan, Z., Tian, C. (eds) Computing and Combinatorics. COCOON 2019. Lecture Notes in Computer Science(), vol 11653. Springer, Cham. https://doi.org/10.1007/978-3-030-26176-4_4

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  • DOI: https://doi.org/10.1007/978-3-030-26176-4_4

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