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19
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 83 (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.
A Deterministic Strongly Polynomial Algorithm for Matrix Scaling and Approximate Permanents
"... We present a deterministic strongly polynomial algorithm that computes the permanent of a nonnegative n x n matrix to within a multiplicative factor of e^n. To this end ..."
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Cited by 63 (8 self)
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We present a deterministic strongly polynomial algorithm that computes the permanent of a nonnegative n x n matrix to within a multiplicative factor of e^n. To this end
Label Ranking by Learning Pairwise Preferences
"... Preference learning is an emerging topic that appears in different guises in the recent literature. This work focuses on a particular learning scenario called label ranking, where the problem is to learn a mapping from instances to rankings over a finite number of labels. Our approach for learning s ..."
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Cited by 46 (16 self)
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Preference learning is an emerging topic that appears in different guises in the recent literature. This work focuses on a particular learning scenario called label ranking, where the problem is to learn a mapping from instances to rankings over a finite number of labels. Our approach for learning such a mapping, called ranking by pairwise comparison (RPC), first induces a binary preference relation from suitable training data using a natural extension of pairwise classification. A ranking is then derived from the preference relation thus obtained by means of a ranking procedure, whereby different ranking methods can be used for minimizing different loss functions. In particular, we show that a simple (weighted) voting strategy minimizes risk with respect to the wellknown Spearman rank correlation. We compare RPC to existing label ranking methods, which are based on scoring individual labels instead of comparing pairs of labels. Both empirically and theoretically, it is shown that RPC is superior in terms of computational efficiency, and at least competitive in terms of accuracy.
Unifying Maximum Cut and Minimum Cut of a Planar Graph
, 1990
"... We consider the realweight maximum cut of a planar graph. Given an undirected planar graph with realvalued weights associated with its edges, find a partition of the vertices into two nonemply sets such that the sum of the weights of the edges connecting the two sets is maximum. The conventional ..."
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Cited by 12 (0 self)
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We consider the realweight maximum cut of a planar graph. Given an undirected planar graph with realvalued weights associated with its edges, find a partition of the vertices into two nonemply sets such that the sum of the weights of the edges connecting the two sets is maximum. The conventional maximum cut and minimum cut problems assume nonnegative edge weights, and thus are special cases of the realweight maximum cut. We develop an O(n3I2 logn) algorithm for finding a realweight maximum cut of a planar graph where n is the number of vertices in the graph. The best maximum cut algorithm previously known for planar graphs has the running time of O(n³).
Comparing mean field and Euclidean matching problems
 Eur. Phys. J. (B
, 1998
"... (will be inserted by the editor) ..."
Unique Maximum Matching Algorithms
, 2002
"... We consider the problem of testing the uniqueness of maximum matchings, both in the unweighted and in the weighted case. For the unweighted case, we have two results. First, given a graph with n vertices and m edges, we can test whether the graph has a unique perfect matching, and find it if it exis ..."
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Cited by 12 (0 self)
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We consider the problem of testing the uniqueness of maximum matchings, both in the unweighted and in the weighted case. For the unweighted case, we have two results. First, given a graph with n vertices and m edges, we can test whether the graph has a unique perfect matching, and find it if it exists, in O(m log^4 n) time. This algorithm uses a recent dynamic connectivity algorithm and an old result of Kotzig characterizing unique perfect matchings in terms of bridges. For the special case of...
Large Exponential Neighbourhoods for the Traveling Salesman Problem
, 1997
"... An exponential neighbourhood for the traveling salesman problem (TSP) is a set of tours, which grows exponentially in the input size. An exponential neighbourhood is polynomial time searchable if we can find the best among the exponential number of tours in polynomial time. Deineko and Woeginger ask ..."
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Cited by 5 (1 self)
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An exponential neighbourhood for the traveling salesman problem (TSP) is a set of tours, which grows exponentially in the input size. An exponential neighbourhood is polynomial time searchable if we can find the best among the exponential number of tours in polynomial time. Deineko and Woeginger asked if there exists polynomial time searchable neighbourhoods of size at least bffnc!, for some ff ? 1 2 , where n is the number of vertices in the TSP. In this paper we prove that such neighbourhoods exist for all ff ! 1. In fact we give a neighbourhood of size at least c n! k n , for any k ? 2 + ln k 1 (i.e. k ? 3:14619:::) and for some constant c (depending on k), which can be searched in O(n 3 ) time. Using a slight variation of the above algorithm we can search neighbourhoods of size bffnc! in time O(n 1+2ff ), for any 0 ! ff ! 1. Deineko and Woeginger proved (indirectly) that if P 6= NP then no algorithm for searching a neighbourhood of size bffnc! can run faster then O(n 1+ff ...
Matching Algorithms and Feature Match Quality Measures For Model Based Object Recognition with Applications to Automatic Target Recognition
 York University
, 1999
"... iii Preface Needless to say, this work would not have been possible without the continuing support of Robert Hummel and Benjamin Goldberg. To them goes my deepest gratitude. iv Table of Contents Acknowledgements............................................................................. iii ..."
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Cited by 2 (0 self)
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iii Preface Needless to say, this work would not have been possible without the continuing support of Robert Hummel and Benjamin Goldberg. To them goes my deepest gratitude. iv Table of Contents Acknowledgements............................................................................. iii