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87
Theoretical improvements in algorithmic efficiency for network flow problems

, 1972
"... This paper presents new algorithms for the maximum flow problem, the Hitchcock transportation problem, and the general minimumcost flow problem. Upper bounds on ... the numbers of steps in these algorithms are derived, and are shown to compale favorably with upper bounds on the numbers of steps req ..."
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Cited by 375 (0 self)
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This paper presents new algorithms for the maximum flow problem, the Hitchcock transportation problem, and the general minimumcost flow problem. Upper bounds on ... the numbers of steps in these algorithms are derived, and are shown to compale favorably with upper bounds on the numbers of steps required by earlier algorithms. First, the paper states the maximum flow problem, gives the FordFulkerson labeling method for its solution, and points out that an improper choice of flow augmenting paths can lead to severe computational difficulties. Then rules of choice that avoid these difficulties are given. We show that, if each flow augmentation is made along an augmenting path having a minimum number of arcs, then a maximum flow in an nnode network will be obtained after no more than ~(n a n) augmentations; and then we show that if each flow change is chosen to produce a maximum increase in the flow value then, provided the capacities are integral, a maximum flow will be determined within at most 1 + logM/(M1) if(t, S) augmentations, wheref*(t, s) is the value of the maximum flow and M is the maximum number of arcs across a cut. Next a new algorithm is given for the minimumcost flow problem, in which all shortestpath computations are performed on networks with all weights nonnegative. In particular, this
The Markov Chain Monte Carlo method: an approach to approximate counting and integration
, 1996
"... In the area of statistical physics, Monte Carlo algorithms based on Markov chain simulation have been in use for many years. The validity of these algorithms depends crucially on the rate of convergence to equilibrium of the Markov chain being simulated. Unfortunately, the classical theory of stocha ..."
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Cited by 234 (12 self)
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In the area of statistical physics, Monte Carlo algorithms based on Markov chain simulation have been in use for many years. The validity of these algorithms depends crucially on the rate of convergence to equilibrium of the Markov chain being simulated. Unfortunately, the classical theory of stochastic processes hardly touches on the sort of nonasymptotic analysis required in this application. As a consequence, it had previously not been possible to make useful, mathematically rigorous statements about the quality of the estimates obtained. Within the last ten years, analytical tools have been devised with the aim of correcting this deficiency. As well as permitting the analysis of Monte Carlo algorithms for classical problems in statistical physics, the introduction of these tools has spurred the development of new approximation algorithms for a wider class of problems in combinatorial enumeration and optimization. The “Markov chain Monte Carlo ” method has been applied to a variety of such problems, and often provides the only known efficient (i.e., polynomial time) solution technique.
Computing MinimumWeight Perfect Matchings
 INFORMS
, 1999
"... We make several observations on the implementation of Edmonds’ blossom algorithm for solving minimumweight perfectmatching problems and we present computational results for geometric problem instances ranging in size from 1,000 nodes up to 5,000,000 nodes. A key feature in our implementation is the ..."
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Cited by 82 (2 self)
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We make several observations on the implementation of Edmonds’ blossom algorithm for solving minimumweight perfectmatching problems and we present computational results for geometric problem instances ranging in size from 1,000 nodes up to 5,000,000 nodes. A key feature in our implementation is the use of multiple search trees with an individual dualchange � for each tree. As a benchmark of the algorithm’s performance, solving a 100,000node geometric instance on a 200 Mhz PentiumPro computer takes approximately 3 minutes.
The alldifferent Constraint: A Survey
, 2001
"... The constraint of difference is known to the constraint programming community since Lauriere introduced Alice in 1978. Since then, several strategies have been designed to solve the alldifferent constraint. This paper surveys the most important developments over the years regarding the alldifferent ..."
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Cited by 41 (1 self)
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The constraint of difference is known to the constraint programming community since Lauriere introduced Alice in 1978. Since then, several strategies have been designed to solve the alldifferent constraint. This paper surveys the most important developments over the years regarding the alldifferent constraint. First we summarize the underlying concepts and results from graph theory and integer programming. Then we give an overview and an abstract comparison of different solution strategies. In addition, the symmetric alldifferent constraint is treated. Finally, we show how to apply costbased filtering to the alldifferent constraint.
Helios: a hybrid electrical/optical switch architecture for modular data centers
 in ACM SIGCOMM ‘10
"... The basic building block of ever larger data centers has shifted from a rack to a modular container with hundreds or even thousands of servers. Delivering scalable bandwidth among such containers is a challenge. A number of recent efforts promise full bisection bandwidth between all servers, though ..."
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Cited by 40 (11 self)
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The basic building block of ever larger data centers has shifted from a rack to a modular container with hundreds or even thousands of servers. Delivering scalable bandwidth among such containers is a challenge. A number of recent efforts promise full bisection bandwidth between all servers, though with significant cost, complexity, and power consumption. We present Helios, a hybrid electrical/optical switch architecture that can deliver significant reductions in the number of switching elements, cabling, cost, and power consumption relative to recently proposed data center network architectures. We explore architectural trade offs and challenges associated with realizing these benefits through the evaluation of a fully functional Helios prototype.
Graph construction and bmatching for semisupervised learning
 In International Conference on Machine Learning
"... Graph based semisupervised learning (SSL) methods play an increasingly important role in practical machine learning systems. A crucial step in graph based SSL methods is the conversion of data into a weighted graph. However, most of the SSL literature focuses on developing label inference algorithm ..."
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Cited by 40 (9 self)
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Graph based semisupervised learning (SSL) methods play an increasingly important role in practical machine learning systems. A crucial step in graph based SSL methods is the conversion of data into a weighted graph. However, most of the SSL literature focuses on developing label inference algorithms without extensively studying the graph building method and its effect on performance. This article provides an empirical study of leading semisupervised methods under a wide range of graph construction algorithms. These SSL inference algorithms include the Local and Global Consistency (LGC) method, the Gaussian Random Field (GRF) method, the Graph Transduction via Alternating Minimization (GTAM) method as well as other techniques. Several approaches for graph construction, sparsification and weighting are explored including the popular knearest neighbors method (kNN) and the bmatching method. As opposed to the greedily constructed kNN graph, the bmatched graph ensures each node in the graph has the same number of edges and produces a balanced or regular graph. Experimental results on both artificial data and real benchmark datasets indicate that bmatching produces more robust graphs and therefore provides significantly better prediction accuracy without any significant change in computation time.
MATCHING, EULER TOURS AND THE CHINESE POSTMAN
 MATHEMATICAL PROGRAMMING 5 (1973) 88124. NORTHHOLLAND PUBLISHING COMPANY
, 1973
"... The solution of the Chinese postman problem using matching theory is given. The convex hull of integer solutions is described as a linear programming polyhedron. This polyhedron is used to show that a good algorithm gives an optimum solution. The algorithm is a specialization of the more general bm ..."
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Cited by 29 (0 self)
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The solution of the Chinese postman problem using matching theory is given. The convex hull of integer solutions is described as a linear programming polyhedron. This polyhedron is used to show that a good algorithm gives an optimum solution. The algorithm is a specialization of the more general bmatching blossom algorithm. Algorithms for finding Euler tours and related problems are also discussed.
Distributed Weighted Matching
 In 18th DISC (Amsterdam, the Netherlands, 2004), R. Guerraoui (Ed.), LNCS 3274
, 2003
"... In this paper, we present fast and fully distributed algorithms for matching in weighted trees and general weighted graphs. The time complexity as well as the approximation ratio of the tree algorithm is constant. In particular, the approximation ratio is 4. For the general graph algorithm we pro ..."
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Cited by 27 (2 self)
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In this paper, we present fast and fully distributed algorithms for matching in weighted trees and general weighted graphs. The time complexity as well as the approximation ratio of the tree algorithm is constant. In particular, the approximation ratio is 4. For the general graph algorithm we prove a constant ratio bound of 5 and a polylogarithmic time complexity of O(log n).
ON THE COMPLEXITY OF APPROXIMATING kSET PACKING
 COMPUTATIONAL COMPLEXITY
, 2006
"... Given a kuniform hypergraph, the Maximum kSet Packing problem is to find the maximum disjoint set of edges. We prove that this problem cannot be efficiently approximated to within a factor of Ω(k / ln k) unless P = NP. This improves the previous hardness of approximation factor of k/2 O( √ ln k) ..."
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Cited by 22 (0 self)
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Given a kuniform hypergraph, the Maximum kSet Packing problem is to find the maximum disjoint set of edges. We prove that this problem cannot be efficiently approximated to within a factor of Ω(k / ln k) unless P = NP. This improves the previous hardness of approximation factor of k/2 O( √ ln k) by Trevisan. This result extends to the problem of kDimensionalMatching.