Given an unknown tournament over {1.....n}, we show that the query complexity of the question "Is there a vertex with outdegree n - 1 ?" (known as a Condorcet winner in social choice theory) is exactly 2n - ...
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Given an unknown tournament over {1.....n}, we show that the query complexity of the question "Is there a vertex with outdegree n - 1 ?" (known as a Condorcet winner in social choice theory) is exactly 2n - [log(n)] - 2. This stands in stark contrast to the evasiveness of this property in general digraphs. (C) 2008 Elsevier B.V. All rights reserved.
We consider inapproximability of the correlation clustering problem defined as follows: Given a graph G = (V. E) where each edge is labeled either "+" (similar) or "-" (dissimilar), correlation clu...
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We consider inapproximability of the correlation clustering problem defined as follows: Given a graph G = (V. E) where each edge is labeled either "+" (similar) or "-" (dissimilar), correlation clustering seeks to partition the vertices into Clusters so that the number of pairs correctly (resp., incorrectly) classified with respect to the labels is maximized (resp., minimized). The two complementary problems are called MAxAGREE and MINDISAGREE, respectively, and have been studied on complete graphs, where every edge is labeled. and general graphs, where some edge might not have been labeled. Natural edge-weighted versions of both problems have been studied as well. Let S-MAXAGREE denote the weighted problem where all weights are taken from set S, we show that S-MAXAGREE with weights bounded by O(vertical bar V vertical bar(1/2-delta)) essentially belongs to the same hardness class in the following sense: if there is a polynomial time algorithm that approximates S-MAXAGREE within a factor of X = O (log vertical bar V vertical bar) with high probability. then for any choice of S', S'-MAXAGREE can be approximated in polynomial time within a factor of (lambda + epsilon), where epsilon > 0 can be arbitrarily small, with high probability. A similar statement also holds for S-MINDISAGREE. This result implies it is hard (assuming NP not equal RP) to approximate unweighted MAXAGREE within a factor of 80/79 - epsilon, improving upon a previous known factor of 116/115 - epsilon by Charikar et al. [M. Charikar, V. Guruswami, A. Wirth. Clustering with qualitative information, journal of Computer and System Sciences 71 (2005) 360-383]. (c) 2008 Elsevier B.V. All rights reserved.
In this note we observe that the problem of mixed graph coloring can be solved in linear time for trees, which improves the quadratic algorithm of Hansen et al. [P. Hansen, J. Kuplinsky, D. de Werra, Mixed graph color...
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In this note we observe that the problem of mixed graph coloring can be solved in linear time for trees, which improves the quadratic algorithm of Hansen et al. [P. Hansen, J. Kuplinsky, D. de Werra, Mixed graph colorings, Math. Methods Oper. Res. 45 (1997) 145 - 160]. (c) 2007 Elsevier B.V. All rights reserved.
We introduce and solve a problem motivated by integrity verification in third-party data distribution: Given all Undirected tree. find a minimum-cardinality set of simple paths that cover all the tree edges and, secon...
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We introduce and solve a problem motivated by integrity verification in third-party data distribution: Given all Undirected tree. find a minimum-cardinality set of simple paths that cover all the tree edges and, secondarily, have smallest total path lengths. We give a linear time algorithm for this problem. (C) 2008 Elsevier B.V. All rights reserved.
algorithms to calculate the fractal dimension of a complex network are presented. One of the algorithms is applied to a parametrized class of models whose fractal dimension transitions from one to two. For the system ...
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algorithms to calculate the fractal dimension of a complex network are presented. One of the algorithms is applied to a parametrized class of models whose fractal dimension transitions from one to two. For the system size we considered here (16384 nodes), the transition takes place from one at p = 0 to essentially two at the small value p = 0.03. This seems to indicate that the transition is likely to become infinitely sharp and occur at p = 0 as the system size increases to infinity.
Given a biconnected graph G with n nodes and a pair of unique nodes s and t, an st-ordering assigns s with 1 and t with n, and every other node with an integer between 2 and n - 1 (inclusive) such that it has at least...
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Given a biconnected graph G with n nodes and a pair of unique nodes s and t, an st-ordering assigns s with 1 and t with n, and every other node with an integer between 2 and n - 1 (inclusive) such that it has at least one neighbor with a smaller number and at least one neighbor with a larger number. This paper presents a self-stabilizing distributed algorithm which assigns an st-ordering to G. The algorithm is shown to require at most O(n log n) rounds to converge to a correct solution.
The k-connectivity problem is to find a minimum-cost k-edge-or k-vertex-connected spanning subgraph of an edge-weighted, undirected graph G for any given G and k. Here, we consider its NP-hard subproblems with respect...
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The k-connectivity problem is to find a minimum-cost k-edge-or k-vertex-connected spanning subgraph of an edge-weighted, undirected graph G for any given G and k. Here, we consider its NP-hard subproblems with respect to the parameter beta, with 1/2 < beta < 1, where G = (V, E) is a complete graph with a cost function c satisfying the sharpened triangle inequality c({u, v}) <= beta . (c({u, w})+ c({w, v})) for all u, v, w is an element of V. First, we give a simple linear-time approximation algorithm for these optimization problems with approximation ratio beta/1-beta for any 1/2 <= beta < 1, which improves the known approximation ratios for 1/2 < beta < 2/3. The analysis of the algorithm above is based on a rough combinatorial argumentation. As the main result of this paper, for k = 3, we sophisticate the combinatorial consideration in order to design a (1 + 5(2 beta-1)/9(1-beta) + O(1/vertical bar V vertical bar))-approximation algorithm for the 3-connectivity problem on graphs satisfying the sharpened triangle inequality for 1/2 <= beta <= 23. As part of the proof, we show that for each spanning 3-edge-connected subgraph H, there exists a spanning 3-regular 2-vertex-connected subgraph H' of at most the same cost, and H can be transformed into H' efficiently. (C) 2008 Elsevier B. V. All rights reserved.
We are interested in finding bounds for the distant-2 chromatic number of geometric graphs drawn from different models. We consider two undirected models of random graphs: random geometric graphs and random proximity ...
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We are interested in finding bounds for the distant-2 chromatic number of geometric graphs drawn from different models. We consider two undirected models of random graphs: random geometric graphs and random proximity graphs for which sharp connectivity thresholds have been shown. We are interested in a.a.s. connected graphs close just above the connectivity threshold. For such subfamilies of random graphs we show that the distant-2-chromatic number is Theta (log n) with high probability. The result on random geometric graphs is extended to the random sector graphs defined in [J. Diaz, J. Petit, M. Serna. A random graph model for optical networks of sensors, IEEE Transactions on Mobile Computing 2 (2003) 143 - 154]. (c) 2007 Elsevier B.V. All rights reserved.
Recently, Lindner showed that every partial 4-cycle system of order n and index 1 could be embedded in a 4-cycle system of order nu and index 1 with nu = 8 [graphICS] + 7, nu = 8 [graphICS] + 8. This improves on the b...
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Recently, Lindner showed that every partial 4-cycle system of order n and index 1 could be embedded in a 4-cycle system of order nu and index 1 with nu <= 2n + 15. While the technique he used does not immediately extend to any higher index, here we develop his ideas to show that every partial 4-cycle system of order n and index. can be embedded in a 4-cycle system of order nu and index. for all lambda-admissible nu >= 8 [graphICS] + 7, nu = 8 [graphICS] + 8. This improves on the best known bounds of nu = 4n and nu = 8n + 1 when lambda > 1 is even and odd respectively.
Given a transportation network having source nodes with evacuees and destination nodes, we want to find a contraflow network configuration (that is, ideal direction for each edge) to minimize the evacuation time. Cont...
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Given a transportation network having source nodes with evacuees and destination nodes, we want to find a contraflow network configuration (that is, ideal direction for each edge) to minimize the evacuation time. Contraflow lane reversal is considered a potential remedy to reduce congestion during evacuations in the context of homeland security and natural disasters (for example, hurricanes). This problem is computationally challenging because of the very large search space and the expense of calculating the evacuation time on a given network. To our knowledge, this paper presents the first macroscopic approaches for the solution of a contraflow network reconfiguration incorporating road capacity constraints, multiple sources, congestion, and scalability. We formally define the contraflow problem based on graph theory and provide a framework of computational structure to classify our approaches. A Greedy heuristic is designed to produce high-quality solutions with significant performance. A Bottleneck Relief heuristic is developed to deal with large numbers of evacuees. We evaluate the proposed approaches both analytically and experimentally using real-world data sets. Experimental results show that our contraflow approaches can reduce the evacuation time by 40 percent or more.
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