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Local T-Spanners with Respect to a Family of Convex Regions

Mousavi, Azadeh Sadat | 2018

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 51170 (19)
  4. University: Sharif University of Technology
  5. Department: Computer Engineering
  6. Advisor(s): Abam, Mohammad Ali
  7. Abstract:
  8. A geometric network on a set V of points in d-dimensional Euclidean space is a weighted undirected graph G(V,E) with vertex set V such that the weight of an edge is the Euclidean distance between its endpoints. We say that the geometric network G(V,E) is a t-spanner of V, for a t > 1, if for each pair of points u and v in V there exists a path in G between u and v of length at most t times the Euclidean distance between u and v. In this thesis, we introduce the new concept of local t-spanners and present some algorithms to construct these geometric graphs. Suppose Gc(V ) is a complete graph and F is a family of convex regions, for instance set of half planes, squares and circles. The graph G, is a local t-spanner with respect to F, if for any R 2 F, the graph G \ R is a t-spanner for Gc(V ) \ R.In the first two chapters, we have introduction and definitions on the context of geometric networks and spanners and we introduce the problem. In the next chapter we have a survey on the past works on the context of t-spanners. In the fourth chapter we provide some examples to show the output of these algorithms are not local t-spanner. Then we construct local t-spanners. At first constructions we only use the input points and we construct local t-spanners with respect to a family of slabs with size of O(n log n), a family of cones with size of O(n log2 n), a family of circles with size of Σ (jAij + jBij) and finally we construct local t-spanner with respect to family of circles with size O(n log2 n) using a linear number of Steiner points. The algorithm runs in O(n log2 n) time
  9. Keywords:
  10. Geometric Networks ; T-Spanner ; T-Path ; Strength Factor ; Local Spanner

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