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Matroids
, 2009
"... One of the primary goals of pure mathematics is to identify common patterns that occur in disparate circumstances, and to create unifying abstractions which identify commonalities and provide a useful framework for further theorems. For example the pattern of an associative operation with inverses a ..."
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One of the primary goals of pure mathematics is to identify common patterns that occur in disparate circumstances, and to create unifying abstractions which identify commonalities and provide a useful framework for further theorems. For example the pattern of an associative operation with inverses and an identity occurs frequently, and gives rise to the notion of an abstract group. On top of the basic axioms of a group, a vast
The optimal pathmatching problem
 COMBINATORICA
, 1997
"... We describe a common generalization of the weighted matching problem and the weighted matroid intersection problem. In this context we establish common generalizations of the main results on those two problemspolynomialtime solvability, minmax theorems, and totally dual integral polyhedral descr ..."
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Cited by 24 (2 self)
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We describe a common generalization of the weighted matching problem and the weighted matroid intersection problem. In this context we establish common generalizations of the main results on those two problemspolynomialtime solvability, minmax theorems, and totally dual integral polyhedral
MATROID INTERSECTION WITH PRIORITY CONSTRAINTS
, 2013
"... In this paper, we consider the following variant of the matroid intersection problem. We are given two matroids M1,M2 on the same ground set E and a subset A of E. Our goal is to find a common independent set I ofM1,M2 such that I ∩A  is maximum among all common independent sets ofM1,M2 and such ..."
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In this paper, we consider the following variant of the matroid intersection problem. We are given two matroids M1,M2 on the same ground set E and a subset A of E. Our goal is to find a common independent set I ofM1,M2 such that I ∩A  is maximum among all common independent sets ofM1,M2
An Algebraic Algorithm for Weighted Linear Matroid Intersection
"... We present a new algebraic algorithm for the classical problem of weighted matroid intersection. This problem generalizes numerous wellknown problems, such as bipartite matching, network flow, etc. Our algorithm has running time Õ(nrω−1 W 1+ɛ) for linear matroids with n elements and rank r, where ω ..."
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Cited by 3 (0 self)
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We present a new algebraic algorithm for the classical problem of weighted matroid intersection. This problem generalizes numerous wellknown problems, such as bipartite matching, network flow, etc. Our algorithm has running time Õ(nrω−1 W 1+ɛ) for linear matroids with n elements and rank r, where
Robust Matchings and Matroid Intersections∗
, 2010
"... The METR technical reports are published as a means to ensure timely dissemination of scholarly and technical work on a noncommercial basis. Copyright and all rights therein are maintained by the authors or by other copyright holders, notwithstanding that they have offered their works here electron ..."
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The METR technical reports are published as a means to ensure timely dissemination of scholarly and technical work on a noncommercial basis. Copyright and all rights therein are maintained by the authors or by other copyright holders, notwithstanding that they have offered their works here electronically. It is understood that all persons copying this information will adhere to the terms and constraints invoked by each author’s copyright. These works may not be reposted without the explicit permission of the copyright holder.
The Complexity of Maximum MatroidGreedoid Intersection and Weighted
"... The maximum intersection problem for a matroid and a greedoid, given by polynomialtime oracles, is shown NPhard by expressing the satisfiability of boolean formulas in 3conjunctive normal form as such an intersection. The corresponding approximation problems are shown NPhard for certain approxima ..."
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The maximum intersection problem for a matroid and a greedoid, given by polynomialtime oracles, is shown NPhard by expressing the satisfiability of boolean formulas in 3conjunctive normal form as such an intersection. The corresponding approximation problems are shown NPhard for certain
SOLVING THE LINEAR MATROID PARITY PROBLEM AS A SEQUENCE OF MATROID INTERSECTION PROBLEMS
, 1990
"... In this paper, we present an O(r 4 n) algorithm for the linear matroid parity problem. Our solution technique is to introduce a modest generalization, the nonsimple parity problem, and identify an important subclass of nonsimple parity problems called 'easy ' parity problems which can be ..."
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Cited by 2 (0 self)
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be solved as matroid intersection problems. We then show how to solve any linear matroid parity problem parametrically as a sequence of 'easy ' parity problems. In contrast to other algorithmic work on this problem, we focus on general structural properties of dual solutions rather than on local
The complexity of maximum matroidgreedoid intersection
 DISCRETE APPL. MATH
, 2006
"... The maximum intersection problem for a matroid and a greedoid, given by polynomialtime oracles, is shown NPhard by expressing the satisfiability of boolean formulas in 3conjunctive normal form as such an intersection. Also the corresponding approximation problem is shown NPhard for certain app ..."
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Cited by 1 (0 self)
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The maximum intersection problem for a matroid and a greedoid, given by polynomialtime oracles, is shown NPhard by expressing the satisfiability of boolean formulas in 3conjunctive normal form as such an intersection. Also the corresponding approximation problem is shown NPhard for certain
Concentration Inequalities for Nonlinear Matroid Intersection
, 2012
"... In this work we propose new randomized rounding algorithms for matroid intersection and matroid base polytopes. We prove concentration inequalities for polynomial objective functions and constraints that has numerous applications and can be used in approximation algorithms for ..."
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Cited by 1 (1 self)
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In this work we propose new randomized rounding algorithms for matroid intersection and matroid base polytopes. We prove concentration inequalities for polynomial objective functions and constraints that has numerous applications and can be used in approximation algorithms for
Lectures on matroids and oriented matroids
, 2005
"... These lecture notes were prepared for the Algebraic Combinatorics; in Europe (ACE) Summer School in Vienna, July 2005. ..."
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These lecture notes were prepared for the Algebraic Combinatorics; in Europe (ACE) Summer School in Vienna, July 2005.
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