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35
Lowcomplexity distributed fair scheduling for wireless multihop networks
"... Abstract — Maxmin fair bandwidth allocation is a meaningful objective whenever the level of user satisfaction cannot be clearly expressed as a function of the allocated bandwidth. In this work, we address the issue of approximating maxmin fairness in a wireless network without the requirement for ..."
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Abstract — Maxmin fair bandwidth allocation is a meaningful objective whenever the level of user satisfaction cannot be clearly expressed as a function of the allocated bandwidth. In this work, we address the issue of approximating maxmin fairness in a wireless network without the requirement for networkwide node coordination and we present a lowoverhead greedy distributed algorithm for reaching this goal. The algorithm is based on distributed computation of a maximum weighted matching based on appropriately defined flow weights and subsequent scheduling of link flows in an effort to provide maxmin rates to them. An inherent feature of our approach is its immunity to topology changes as well as to flow traffic variations. Our method is shown to outperform significantly the centralized (yet, conservative) algorithm of maxmin fair rate computation in general topologies in terms of total resulting throughput, minimum shares and node resource utilization. I.
Scaling algorithms for approximate and exact maximum weight matching
, 2011
"... The maximum cardinality and maximum weight matching problems can be solved in time Õ(m √ n), a bound that has resisted improvement despite decades of research. (Here m and n are the number of edges and vertices.) In this article we demonstrate that this “m √ n barrier ” is extremely fragile, in the ..."
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The maximum cardinality and maximum weight matching problems can be solved in time Õ(m √ n), a bound that has resisted improvement despite decades of research. (Here m and n are the number of edges and vertices.) In this article we demonstrate that this “m √ n barrier ” is extremely fragile, in the following sense. For any ɛ> 0, we give an algorithm that computes a (1 − ɛ)approximate maximum weight matching in O(mɛ −1 log ɛ −1) time, that is, optimal linear time for any fixed ɛ. Our algorithm is dramatically simpler than the best exact maximum weight matching algorithms on general graphs and should be appealing in all applications that can tolerate a negligible relative error. Our second contribution is a new exact maximum weight matching algorithm for integerweighted bipartite graphs that runs in time O(m √ n log N). This improves on the O(Nm √ n)time and O(m √ n log(nN))time algorithms known since the mid 1980s, for 1 ≪ log N ≪ log n. Here N is the maximum integer edge weight. 1
A Simpler Linear Time 2/3  ε Approximation for Maximum Weight Matching
 INF.PROCESS.LETT
"... We present two 2/3  ε approximation algorithms for the maximum weight matching problem that run in time O m log . We give a simple and practical randomized algorithm and a somewhat more complicated deterministic algorithm. Both algorithms are exponentially faster in terms of ..."
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We present two 2/3  &epsilon; approximation algorithms for the maximum weight matching problem that run in time O m log . We give a simple and practical randomized algorithm and a somewhat more complicated deterministic algorithm. Both algorithms are exponentially faster in terms of than a recent algorithm by Drake and Hougardy. We also show that our algorithms can be generalized to find a 1 approximatation to the maximum weight matching, for any > 0.
Algebraic Distance on Graphs
"... Measuring the connection strength between a pair of vertices in a graph is one of the most vital concerns in many graph applications. Simple measures such as edge weights may not be sufficient for capturing the local connectivity. In this paper, we consider a neighborhood of each graph vertex and pr ..."
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Measuring the connection strength between a pair of vertices in a graph is one of the most vital concerns in many graph applications. Simple measures such as edge weights may not be sufficient for capturing the local connectivity. In this paper, we consider a neighborhood of each graph vertex and propagate a certain property value through direct neighbors. We present a measure of the connection strength (called the algebraic distance, see [21]) defined from an iterative process based on this consideration. The proposed measure is attractive in that the process is simple, linear, and easily parallelized. A rigorous analysis of the convergence property of the process confirms the underlying intuition that vertices are mutually reinforced and that the local neighborhoods play an important role in influencing the vertex connectivity. We demonstrate the practical effectiveness of the proposed measure through several combinatorial optimization problems on graphs and hypergraphs. 1
Maximizing Cooperative Diversity Energy Gain for Wireless Networks
, 2007
"... We are concerned with optimally grouping active mobile users in a twouserbased cooperative diversity system to maximize the cooperative diversity energy gain in a radio cell. The optimization problem is formulated as a nonbipartite weightedmatching problem in a static network setting. The weighte ..."
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We are concerned with optimally grouping active mobile users in a twouserbased cooperative diversity system to maximize the cooperative diversity energy gain in a radio cell. The optimization problem is formulated as a nonbipartite weightedmatching problem in a static network setting. The weightedmatching problem can be solved using maximum weighted (MW) matching algorithm in polynomial time O(n 3). To reduce the implementation and computational complexity, we develop a WorstLinkFirst (WLF) matching algorithm, which gives the user with the worse channel condition and the higher energy consumption rate a higher priority to choose its partner. The computational complexity of the proposed WLF algorithm is O(n 2) while the achieved average energy gain is only slightly lower than that of the optimal maximum weightedmatching algorithm and similar to that of the 1/2approximation Greedy matching algorithm (with computational complexity of O(n 2 log n)) for a staticuser network. We further investigate the optimal matching problem in mobile networks. By intelligently applying user mobility information in the matching algorithm, high cooperative diversity energy gain with moderate overhead is possible. In mobile networks, the proposed WLF matching algorithm, being less complex than the MW and the Greedy matching algorithms, yields performance characteristics close to those of the MW matching algorithm and better than the Greedy matching algorithm.
Computing steiner minimum trees in Hamming metric
 In Proceedings of the seventeenth annual ACMSIAM symposium on Discrete algorithm
, 2006
"... Computing Steiner minimum trees in Hamming metric is a well studied problem that has applications in several fields of science such as computational linguistics and computational biology. Among all methods for finding such trees, algorithms using variations of a branch and bound method developed by ..."
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Computing Steiner minimum trees in Hamming metric is a well studied problem that has applications in several fields of science such as computational linguistics and computational biology. Among all methods for finding such trees, algorithms using variations of a branch and bound method developed by Penny and Hendy have been the fastest for more than 20 years. In this paper we describe a new pruning approach that is superior to previous methods and its implementation. 1
A Computationally Efficient 3D Shape Rejection Algorithm
 Proc. ICME 2005,Amsterdam, The
, 2005
"... In this paper, we present an efficient 3D shape rejection algorithm for unlabeled 3D markers. The problem is important in domains such as rehabilitation and the performing arts. There are three key innovations in our approach – (a) a multiresolution shape representation using Haar wavelets for unla ..."
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In this paper, we present an efficient 3D shape rejection algorithm for unlabeled 3D markers. The problem is important in domains such as rehabilitation and the performing arts. There are three key innovations in our approach – (a) a multiresolution shape representation using Haar wavelets for unlabeled markers, (b) a multiresolution shape metric and (c) a shape rejection algorithm that is predicated on the simple idea that we do not need to compute the entire distance to conclude that two shapes are dissimilar. We tested the approach on a realworld pose classification problem with excellent results. We achieved a classification accuracy of 98 % with an order of magnitude improvement in terms of computational complexity over a baseline shape matching algorithm. 1.
LinearTime Approximation for Maximum Weight Matching
"... The maximum cardinality and maximum weight matching problems can be solved in Ã(mân) time, a bound that has resisted improvement despite decades of research. (Here m and n are the number of edges and vertices.) In this article, we demonstrate that this âm â n barrier â can be bypassed by ap ..."
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The maximum cardinality and maximum weight matching problems can be solved in Ã(mân) time, a bound that has resisted improvement despite decades of research. (Here m and n are the number of edges and vertices.) In this article, we demonstrate that this âm â n barrier â can be bypassed by approximation. For any É> 0, we give an algorithm that computes a (1 â É)approximate maximum weight matching in O(mÉâ1 log Éâ1) time, that is, optimal linear time for any fixed É. Our algorithm is dramatically simpler than the best exact maximum weight matching algorithms on general graphs and should be appealing in all applications that can tolerate a negligible relative error.
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 1 Fast Combinatorial Vector Field Topology
"... Abstract—This paper introduces a novel approximation algorithm for the fundamental graph problem of combinatorial vector field topology (CVT). CVT is a combinatorial approach based on a sound theoretical basis given by Forman’s work on a discrete Morse theory for dynamical systems. A computational f ..."
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Abstract—This paper introduces a novel approximation algorithm for the fundamental graph problem of combinatorial vector field topology (CVT). CVT is a combinatorial approach based on a sound theoretical basis given by Forman’s work on a discrete Morse theory for dynamical systems. A computational framework for this mathematical model of vector field topology has been developed recently. The applicability of this framework is however severely limited by the quadratic complexity of its main computational kernel. In this work we present an approximation algorithm for CVT with a significantly lower complexity. This new algorithm reduces the runtime by several orders of magnitude, and maintains the main advantages of CVT over the continuous approach. Due to the simplicity of our algorithm it can be easily parallelized to improve the runtime further.
A Measure of the Connection Strengths between Graph Vertices with Applications
, 909
"... We present a simple iterative strategy for measuring the connection strength between a pair of vertices in a graph. The method is attractive in that it has a linear complexity and can be easily parallelized. Based on an analysis of the convergence property, we propose a mutually reinforcing model to ..."
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We present a simple iterative strategy for measuring the connection strength between a pair of vertices in a graph. The method is attractive in that it has a linear complexity and can be easily parallelized. Based on an analysis of the convergence property, we propose a mutually reinforcing model to explain the intuition behind the strategy. The practical effectiveness of this measure is demonstrated through several combinatorial optimization problems on graphs and hypergraphs. 1