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Fault-Tolerant Additive Weighted Geometric Spanners

  • Sukanya Bhattacharjee
  • R. InkuluEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11394)

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(pq) is the (geodesic) Euclidean distance between p and q. For a real number \(t > 1\), a graph G(SE) 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 (kt)-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 points in S belonging to either \(\mathbb {R}^d\) or located in the given simple polygon. Note that d(pq) is the geodesic Euclidean distance between p and q in the case of simple polygons whereas in the case of \(\mathbb {R}^d\) it is the Euclidean distance along the line segment joining p and q.

Keywords

Computational geometry Geometric spanners Approximation algorithms 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringIIT GuwahatiGuwahatiIndia

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