In this paper, we first show how a certain ordering of vertices, called bicompatible elimination ordering (BCO), of a proper interval graph can be used to solve efficiently several problems in proper interval graphs. ...
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In this paper, we first show how a certain ordering of vertices, called bicompatible elimination ordering (BCO), of a proper interval graph can be used to solve efficiently several problems in proper interval graphs. We, then, propose an NC parallel algorithm (i.e., polylogarithmic-time employing a polynomial number of processors) in SIMD CRCW PRAM (Single Instruction Stream Multiple Data Stream Concurrent Read Concurrent Write Parallel Random Access Machine) model of parallel computation to compute a BCO of a proper interval graph. To the best of our knowledge, this is the first NC parallel algorithm to compute a BCO of a proper interval graph. (C) 2009 Elsevier B.V. All rights reserved.
We present new results for the Stochastic Shortest Path problem when an unlimited number of hops may be used. Nodes and links in the network may be congested or uncongested, and their states change over time. The goal...
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We present new results for the Stochastic Shortest Path problem when an unlimited number of hops may be used. Nodes and links in the network may be congested or uncongested, and their states change over time. The goal is to adaptively choose the next node to visit such that the expected cost to the destination is minimized. Since the state of a node may change, having the option to revisit a node can improve the expected cost. Therefore, the option to use an unbounded number of hops may be required to achieve the minimum expected cost. We show that when revisits are prohibited, the optimal routing problem is NP-hard. We also prove properties about networks for which continual improvement may occur. We study the related routing problem which asks whether it is possible to determine the optimal next node based on the current node and state, when an unlimited number of hops is allowed. We show that as the number of hops increases, this problem may not converge to a solution. (C) 2008 Elsevier B.V. All rights reserved.
We show that a maximum-weight triangle in an undirected graph with n vertices and real weights assigned to vertices can be found in time O(n(omega) + n(2+o(1))), where omega is the exponent of the fastest matrix multi...
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We show that a maximum-weight triangle in an undirected graph with n vertices and real weights assigned to vertices can be found in time O(n(omega) + n(2+o(1))), where omega is the exponent of the fastest matrix multiplication algorithm. By the currently best bound on omega, the running time of our algorithm is O(n(2.376)). Our algorithm substantially improves the previous time-bounds for this problem, and its asymptotic time complexity matches that of the fastest known algorithm for finding any triangle (not necessarily a maximum-weight one) in a graph. We can extend our algorithm to improve the upper bounds on finding a maximum-weight triangle in a sparse graph and on finding a maximum-weight subgraph isomorphic to a fixed graph. We can find a maximum-weight triangle in a vertex-weighted graph with m edges in asymptotic time required by the fastest algorithm for finding any triangle in a graph with m edges, i.e., in time O(m(1.41)). Our algorithms for a maximum-weight fixed subgraph (in particular any clique of constant size) are asymptotically as fast as the fastest known algorithms for a fixed subgraph.
This article reports the results of an extensive experimental analysis of efficient algorithms for computing graph spanners in the data streaming model, where an (alpha, beta)-spanner of a graph G is a subgraph S subs...
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This article reports the results of an extensive experimental analysis of efficient algorithms for computing graph spanners in the data streaming model, where an (alpha, beta)-spanner of a graph G is a subgraph S subset of G such that for each pair of vertices the distance in S is at most a times the distance in G plus beta. To the best of our knowledge, this is the first computational study of graph spanner algorithms in a streaming setting. We compare experimentally the randomized algorithms proposed by Baswana (http://***/abstract?id=oai:***:cs/0611023) and by Elkin (In: Proceedings of the 34th International Colloquium on Automata, Languages and Programming (ICALP 2007), Wroclaw, Poland, pp. 716-727, 9-13 July 2007) for general stretch factors with the deterministic algorithm presented by Ausiello et al. (In: Proceedings of the 15th Annual European Symposium on algorithms (ESA 2007), Engineering and Applications Track, Eilat, Israel, 8-10 October 2007. LNCS, vol. 4698, pp. 605-617, 2007), designed for building small stretch spanners. All the algorithms we implemented work in a data streaming model where the input graph is given as a stream of edges in arbitrary order, and all of them need a single pass over the data. Differently from the algorithm in Ausiello et al., the algorithms in Baswana (http://***/abstract?id=oai:***:cs/0611023) and Elkin (In: Proceedings of the 34th International Colloquium on Automata, Languages and Programming (ICALP 2007), Wroclaw, Poland, pp. 716-727, 9-13 July 2007) need to know in advance the number of vertices in the graph. The results of our experimental investigation on several input families confirm that all these algorithms are very efficient in practice, finding spanners with stretch and size much smaller than the theoretical bounds and comparable to those obtainable by off-line algorithms. Moreover, our experimental findings confirm that small values of the stretch factor are the case of
Based on the mobile automaton model, an algorithm is introduced that grows planar, trivalent graphs by exhibiting a peculiar, twofold dynamics. In a first phase, graph growth appears to be pseudo-random and O(n) then ...
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Based on the mobile automaton model, an algorithm is introduced that grows planar, trivalent graphs by exhibiting a peculiar, twofold dynamics. In a first phase, graph growth appears to be pseudo-random and O(n) then it settles to a very regular behavior and O(root n) rate. A pseudo-random O(root n) mobile automaton is already known;the new automaton provides now a finite, but surprisingly long, pseudo-random, linear growth process. Applications of mobile automata to fundamental physics and quantum gravity have been recently suggested. (C) 2009 Elsevier B.V. All rights reserved.
In this paper, the mutual exclusion scheduling problem is addressed. Given a simple and undirected graph G and an integer k, the problem is to find a minimum coloring of G such that each color is used at most k times....
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In this paper, the mutual exclusion scheduling problem is addressed. Given a simple and undirected graph G and an integer k, the problem is to find a minimum coloring of G such that each color is used at most k times. When restricted to interval graphs or related classes like circular-arc graphs and tolerance graphs, the problem has some applications in workforce planning. Unfortunately, the problem is shown to be NP-hard for interval graphs, even if k is a constant greater than or equal to four [H.L. Bodlaencler and K. Jansen Restrictions of graph partition problems. Part 1, Theoretical Computer Science 148(1995) pp. 93-109]. Several polynomial-time solvable cases significant in practice are exhibited here, for which we took care to devise simple and efficient algorithms (in particular linear-time and space algorithms). On the other hand, by reinforcing the NP-hardness result of Bodlaender and Jansen, we obtain a more precise cartography of the complexity of the problem for the classes of graphs studied. (c) 2008 Elsevier B.V. All rights reserved.
The procedures Studied in this paper originate from a problem posed at the International Mathematical Olympiad in 1986. We present several approaches to the IMO problem and its generalizations. In this context we intr...
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The procedures Studied in this paper originate from a problem posed at the International Mathematical Olympiad in 1986. We present several approaches to the IMO problem and its generalizations. In this context we introduce a "signed mean value procedure" and study "relaxation procedures on graphs". We prove that these processes are always finite, thus confirming a conjecture of Akiyama, Hosono and Urabe [J. Akiyama, K. Hosono, M. Urabe, Some combinatorial problems. Discrete Mathematics 116 (1993) 291-298]. Moreover, we indicate relations to sorting and to an iterative method used in circle packing. (C) 2008 Elsevier B.V. All rights reserved.
ShaEP is a tool for rigid-body superimposition and similarity evaluation of ligand-sized molecules. Molecular overlay methods traditionally work on either substructures, molecular surfaces or interaction fields, or at...
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ShaEP is a tool for rigid-body superimposition and similarity evaluation of ligand-sized molecules. Molecular overlay methods traditionally work on either substructures, molecular surfaces or interaction fields, or atomcentered Gaussian functions representing the molecular volume. While substructure searches are unlikely to reveal hits that are chemically different from the template structure, the other methods are capable of "scaffold hopping". Methods that match characteristic points in interaction fields can find alignments in situations where only some portions of the structures match but potentially miss good alignments if the used point sets are not detailed enough, which in turn increases the runtime of the used graph algorithms beyond practical limits. The faster, polynomially scaling volumetric methods consider the whole space to be equally important, which works well for molecules of equal size but partial matches might go undetected. ShaEP aims to capture the strengths of both field-based and volumetric approaches. It generates initial superimpositions using a matching algorithm on graphs that coarsely represent the electrostatic potential and local shape at points close to the molecular surfaces. The initial alignments are then optimized by maximization of the volume overlap of the molecules, computed using Gaussian functions. ShaEP overlays drug-sized molecules on a subsecond timescale, allowing for the screening of large virtual libraries. The program is available free of charge from ***/fak/mnf/bkf/research/johnson/***.
The assessment of phylogenetic network reconstruction methods requires the ability to compare phylogenetic networks. This is the first in a series of papers devoted to the analysis and comparison of metrics for tree-c...
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The assessment of phylogenetic network reconstruction methods requires the ability to compare phylogenetic networks. This is the first in a series of papers devoted to the analysis and comparison of metrics for tree-child time-consistent phylogenetic networks on the same set of taxa. In this paper, we study three metrics that have already been introduced in the literature: the Robinson-Foulds distance, the tripartition distance, and the mu-distance. They generalize to networks the classical Robinson-Foulds or partition distance for phylogenetic trees. We analyze the behavior of these metrics by studying their least and largest values and when they achieve them. As a by-product of this study, we obtain tight bounds on the size of a tree-child time-consistent phylogenetic network.
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