Results 1  10
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35
Combinatorial Auctions with Decreasing Marginal Utilities
, 2001
"... This paper considers combinatorial auctions among such submodular buyers. The valuations of such buyers are placed within a hierarchy of valuations that exhibit no complementarities, a hierarchy that includes also OR and XOR combinations of singleton valuations, and valuations satisfying the gross s ..."
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Cited by 137 (21 self)
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This paper considers combinatorial auctions among such submodular buyers. The valuations of such buyers are placed within a hierarchy of valuations that exhibit no complementarities, a hierarchy that includes also OR and XOR combinations of singleton valuations, and valuations satisfying the gross substitutes property. Those last valuations are shown to form a zeromeasure subset of the submodular valuations that have positive measure. While we show that the allocation problem among submodular valuations is NPhard, we present an efficient greedy 2approximation algorithm for this case and generalize it to the case of limited complementarities. No such approximation algorithm exists in a setting allowing for arbitrary complementarities. Some results about strategic aspects of combinatorial auctions among players with decreasing marginal utilities are also presented.
Algorithms in Discrete Convex Analysis
 Math. Programming
, 2000
"... this paper is to describe the f#eA damental results on M and Lconvex f#24L2A+ with special emphasis on algorithmic aspects. ..."
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Cited by 96 (22 self)
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this paper is to describe the f#eA damental results on M and Lconvex f#24L2A+ with special emphasis on algorithmic aspects.
Holographic Algorithms: From Art to Science
 Electronic Colloquium on Computational Complexity Report
, 2007
"... We develop the theory of holographic algorithms. We give characterizations of algebraic varieties of realizable symmetric generators and recognizers on the basis manifold, and a polynomial time decision algorithm for the simultaneous realizability problem. Using the general machinery we are able to ..."
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Cited by 19 (10 self)
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We develop the theory of holographic algorithms. We give characterizations of algebraic varieties of realizable symmetric generators and recognizers on the basis manifold, and a polynomial time decision algorithm for the simultaneous realizability problem. Using the general machinery we are able to give unexpected holographic algorithms for some counting problems, modulo certain Mersenne type integers. These counting problems are #Pcomplete without the moduli. Going beyond symmetric signatures, we define dadmissibility and drealizability for general signatures, and give a characterization of 2admissibility and some general constructions of admissible and realizable families. 1
On the Theory of Matchgate Computations
 Submitted. Also available at Electronic Colloquium on Computational Complexity Report
, 2007
"... Valiant has proposed a new theory of algorithmic computation based on perfect matchings and the Pfaffian. We study the properties of matchgates—the basic building blocks in this new theory. We give a set of algebraic identities which completely characterize these objects in terms of the GrassmannPl ..."
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Cited by 13 (5 self)
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Valiant has proposed a new theory of algorithmic computation based on perfect matchings and the Pfaffian. We study the properties of matchgates—the basic building blocks in this new theory. We give a set of algebraic identities which completely characterize these objects in terms of the GrassmannPlücker identities. In the important case of 4 by 4 matchgate matrices, which was used in Valiant’s classical simulation of a fragment of quantum computations, we further realize a group action on the character matrix of a matchgate, and relate this information to its compound matrix. Then we use Jacobi’s theorem to prove that in this case the invertible matchgate matrices form a multiplicative group. These results are useful in establishing limitations on the ultimate capabilities of Valiant’s theory of matchgate computations and his closely related theory of Holographic Algorithms. 1
Compositionality issues in discrete, continuous, and hybrid systems
 International Journal of Robust and Nonlinear Control
, 2001
"... Compositionality issues in discrete, continuous and hybrid systems A.J. van der Schaft and J.M. Schumacher 1 ..."
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Cited by 11 (2 self)
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Compositionality issues in discrete, continuous and hybrid systems A.J. van der Schaft and J.M. Schumacher 1
Algebraic structures and algorithms for matching and matroid problems
"... We present new algebraic approaches for several wellknown combinatorial problems, including nonbipartite matching, matroid intersection, and some of their generalizations. Our work yields new randomized algorithms that are the most efficient known. For nonbipartite matching, we obtain a simple, pu ..."
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Cited by 10 (2 self)
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We present new algebraic approaches for several wellknown combinatorial problems, including nonbipartite matching, matroid intersection, and some of their generalizations. Our work yields new randomized algorithms that are the most efficient known. For nonbipartite matching, we obtain a simple, purely algebraic algorithm with running time O(n ω) where n is the number of vertices and ω is the matrix multiplication exponent. This resolves the central open problem of Mucha and Sankowski (2004). For matroid intersection, our algorithm has running time O(nr ω−1) for matroids with n elements and rank r that satisfy some natural conditions. This algorithm is based on new algebraic results characterizing the size of a maximum intersection in contracted matroids. Furthermore, the running time of this algorithm is essentially optimal.
Algebraic Algorithms for Matching and Matroid Problems
 SIAM JOURNAL ON COMPUTING
, 2009
"... We present new algebraic approaches for two wellknown combinatorial problems: nonbipartite matching and matroid intersection. Our work yields new randomized algorithms that exceed or match the efficiency of existing algorithms. For nonbipartite matching, we obtain a simple, purely algebraic algori ..."
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Cited by 10 (0 self)
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We present new algebraic approaches for two wellknown combinatorial problems: nonbipartite matching and matroid intersection. Our work yields new randomized algorithms that exceed or match the efficiency of existing algorithms. For nonbipartite matching, we obtain a simple, purely algebraic algorithm with running time O(n ω) where n is the number of vertices and ω is the matrix multiplication exponent. This resolves the central open problem of Mucha and Sankowski (2004). For matroid intersection, our algorithm has running time O(nr ω−1) for matroids with n elements and rank r that satisfy some natural conditions.
Sensor Placement for Fault Isolation in Linear DifferentialAlgebraic Systems
"... An algorithm is proposed for computing which sensor additions that make a diagnosis requirement specification regarding fault detectability and isolability attainable for a given linear differentialalgebraic model. Restrictions on possible sensor locations can be given and if the diagnosis specifi ..."
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Cited by 8 (6 self)
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An algorithm is proposed for computing which sensor additions that make a diagnosis requirement specification regarding fault detectability and isolability attainable for a given linear differentialalgebraic model. Restrictions on possible sensor locations can be given and if the diagnosis specification is not attainable with any available sensor addition, the algorithm provides the solutions that maximize specification fulfillment. Previous approaches with similar objectives have been structural, but since this algorithm is analytical, it can handle models where structural approaches fail. A Mathematica implementation of the algorithm can be downloaded from
The linear deltamatroid parity problem
 J. Comb. Theory B
"... This paper addresses a generalization of the matroid parity problem to deltamatroids. We give a minimax relation, as well as an efficient algorithm, for linearly represented deltamatroids. These are natural extensions of the minimax theorem of Lova ´ sz and the augmenting path algorithm of Gabow an ..."
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Cited by 7 (0 self)
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This paper addresses a generalization of the matroid parity problem to deltamatroids. We give a minimax relation, as well as an efficient algorithm, for linearly represented deltamatroids. These are natural extensions of the minimax theorem of Lova ´ sz and the augmenting path algorithm of Gabow and Stallmann for the linear matroid parity problem.