Spelling suggestions: "subject:"experimental algorithmic"" "subject:"experimental algorithmiques""
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An Experimental Study of Distance Sensitivity OraclesWilliams, Vincent Troy 26 October 2010 (has links)
The paper \A Nearly Optimal Oracle for Avoiding Failed Vertices and Edges" by
Aaron Bernstein and David Karger lays out a nearly optimal algorithm for nding the
shortest distances and paths between vertices with any given single failure in constant
time without reconstructing the oracle. Using their paper as a guideline, we have
implemented their algorithm in C++ and recorded each step in this thesis. Each step
has its own pseudo-code and its own analysis to prove that the entire oracle construction
stays within the stated running time and total space bounds, from the authors. The
effciency of the algorithm is compared against that of the brute-force methods total
running time and total space needed. Using multiple test cases with an increasing
number of vertices and edges, we have experimentally validated that their algorithm
holds true to their statements of space, running time, and query time.
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Path Centrality: A New Centrality Measure in NetworksAlahakoon, Tharaka 28 May 2010 (has links)
In network analysis, it is useful to identify important vertices in a network. Based on the varying notions of importance of vertices, a number of centrality measures are defined and studied in the literature. Some popular centrality measures, such as betweenness centrality, are computationally prohibitive for large-scale networks. In this thesis, we propose a new centrality measure called k-path centrality and experimentally compare this measure with betweenness centrality.
We present a polynomial-time randomized algorithm for distinguishing high k-path centrality vertices from low k-path centrality vertices in any given (unweighted or weighted) graph. Specifically, for any graph G = (V, E) with n vertices and for every choice of parameters α ∈ (0, 1), ε ∈ (0, 1/2), and integer k ∈ [1, n], with probability at least 1 − 1/n2 our randomized algorithm distinguishes all vertices v ∈ V that have k-path centrality Ck(v) more than nα(1 + 2ε) from all vertices v ∈ V that have k-path centrality Ck(v) less than nα(1 − 2ε). The running time of the algorithm is O(k2ε −2n1−α ln n).
Theoretically and experimentally, our algorithms are (for suitable choices of parameters) significantly faster than the best known deterministic algorithm for computing exact betweenness centrality values (Brandes’ algorithm). Through experimentations on both real and randomly generated networks, we demonstrate that vertices that have high betweenness centrality values also have high k-path centrality values.
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