S. B. Rao and W. D. Smith. Improved approximation schemes for geometrical graphs via "spanners" and "banyans." May 1998. An extended abstract appeared in [20].  Home/Search   Document Details and Download   Summary   Related Articles   Check

....in terms of centrality) hence a randomized algorithm with expected approximation factor 1 follows. 6 Deterministic and randomized shifting of quadtrees have been used in approximate solutions for nearest neighbor queries [8, 9] for which Lemma 3. 2 was established) traveling salesman tours [3, 28], and other problems. Our example here is interesting in that we are not approximating distances but rather a combinatorial quantity. A nice feature of the above algorithm is that it extends to the weighted packing problem (maximizing the sum of the weights of the chosen objects) In some ....

S. B. Rao and W. D. Smith. Improved approximation schemes for geometrical graphs via `spanners' and `banyans'. In Proc. 31st ACM Sympos. Theory Comput., pages 540-550, 1999.

....presented in this paper. By extending the aforementioned techniques to include Steiner points, deriving the decomposition of a minimum cost biconnected Steiner graph into minimal Steiner trees, and using the generalization of (1 ) spanner to include Steiner points called (1 ) banyans in [20, 21], we obtain the first PTAS for minimum cost Steiner biconnectivity and Steiner two edge connectivity. Organization of the paper. Section 2 provides basic terminology used in our approximation schemes. In Section 3 we outline our new PTAS for Euclidean minimum cost biconnectivity. Section 4 ....

....time is O(n s log(n s) n 2 s O(1) The algorithm can be turned into a Las Vegas one without affecting the stated asymptotic time bounds. Although we have used many ideas from [6] in the design of our algorithm, we have chosen the method of picking a random shifted dissection given in [3, 20, 21]. Therefore we can apply almost the same arguments as those used by Rao and Smith [21, Sections 2.2 and 2.3] to derandomize our algorithm at small increase of the cost Theorem 3.3. For every positive there exists a deterministic algorithm running in time n (d= O(1) log n n 2 (d= O(d 2 ....

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S. B. Rao and W. D. Smith. Improved approximation schemes for geometrical graphs via "spanners" and "banyans." May 1998. An extended abstract appeared in [20].

....graph. Geometric spanners were introduced in computational geometry by Chew [27] They have applications in motion planing [28] they were used for approximating the minimum spanning tree [82] and for a fully polynomial time approximation scheme for the traveling salesman and related problems [68, 5]. We present a further application of spanners in walkthrough systems to solve special range searching problems. The problem of constructing an f spanner for a real constant f 1, that has O(n) edges, has been investigated by many researchers [49, 50, 71, 80, 73, 22, 8, 23, 21, 24, 6, 31] Keil ....

S. B. Rao and W. D. Smith. Improved approximation schemes for geometrical graphs via `spanners' and `banyans'. In 30th ACM Symposium on Theory of Computing (STOC'98), pages 540--550, 1998.

.... introduced by Chew [7] They have applications in motion planing [8] they were used for approximating the minimum spanning tree [17] to solve a special searching problem which appears in walkthrough systems [9] and to a fully polynomial time approximation scheme for the TSP and related problems [13]. The problem of constructing a t spanner for a real constant t 1, that has O(n) edges, has been investigated by many researchers. Keil [11] gave a solution for this problem introducing the q graph 1 , which was generalized by Ruppert and Seidel [14] and Arya et al.: 2] to any fixed dimension ....

S. B. Rao and W. D. Smith. Improved approximation schemes for geometrical graphs via `spanners' and `banyans'. In 30th ACM Symposium on Theory of Computing (STOC'98), pages 540--550, 1998.

....for Plane Steiner Tree Problems Ph.D. Thesis Martin Zachariasen Department of Computer Science (DIKU) University of Copenhagen Universitetsparken 1 DK 2100 K benhavn , Denmark March Abstract Topological network design is the process of planning the layout of a network subject to constraints on topology. Applications include the design of transportation and communication networks where the construction costs typically are associated with the ....

.... the full range of algorithms, in particular for the Euclidean problem: Fast greedy heuristics with an O(n log n) worst case running time behaviour, powerful local search algorithms which provide near optimal solutions quickly, and efficient exact algorithms which solve problem instances with more than 2000 terminals to optimality. The new heuristics provide better solutions faster than any other heuristic proposed in the literature and the new exact algorithm solves problem instances which are more than an order of magnitude larger than those previously solved. The efficiency of the proposed ....

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S. B. Rao and W. D. Smith. Improved Approximation Schemes for Geometrical Graphs via "Spanners" and "Banyans". In Proc. Thirtieth Annual ACM Symposium on Theory of Computing, to appear.

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S. Rao and W. D. Smith. Improved approximation schemes for geometrical graphs via spanners and banyans. In Proceedings of the 30th Annual ACM Symposium on Theory of Computing, pages 540-550, 1998.

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S. B. Rao and W. D. Smith. Improved approximation schemes for geometrical graphs via "spanners" and "banyans." May 1998. An extended abstract appeared in [20].

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