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Printed in USA. COMBINATORIAL OPTIMIZATION WITH RATIONAL OBJECTIVE FUNCTIONS*
, 1979
"... Let A be the problem of minimizing clxl +... + c,x, subject to certain constraints on x = (x,,..., x,), and let B be the problem of minimizing (a, + a,xl +... + o,,x,)/(b, + b,x, +... + b,x,) subject to the same constraints, assuming the denominator is always positive. It is shown that if A is solva ..."
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Let A be the problem of minimizing clxl +... + c,x, subject to certain constraints on x = (x,,..., x,), and let B be the problem of minimizing (a, + a,xl +... + o,,x,)/(b, + b,x, +... + b,x,) subject to the same constraints, assuming the denominator is always positive. It is shown that if A is solvable within O[p(n)] comparisons and O[q(n)] additions, then B is solvable in time O[p(n)(q(n) +p(n))]. This applies to most of the "network" algorithms. Consequently, minimum ratio cycles, minimum ratio spanning trees, minimum ratio (simple) paths, maximum ratio weighted matchings, etc., can be computed withing polynomialtime in the number of variables. This improves a result of E. L. Lawler, namely, that a minimum ratio cycle can be computed within a time bound which is polynomial in the number of bits required to specify an instance of the problem. A recent result on minimum ratio spanning trees by R. Chandrasekaran is also improved by the general arguments presented in this paper. Algorithms of timecomplexity O(IEJ. I vJ2. log1 VJ) for a minimum ratio cycle and O(IE1. log21 VJ.log IoglVI) for a minimum ratio spanning tree are developed. 1. Introduction. Numerous
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 557 (12 self)
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We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized
Implications of rational inattention
 JOURNAL OF MONETARY ECONOMICS
, 2002
"... A constraint that actions can depend on observations only through a communication channel with finite Shannon capacity is shown to be able to play a role very similar to that of a signal extraction problem or an adjustment cost in standard control problems. The resulting theory looks enough like fa ..."
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Cited by 514 (10 self)
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familiar dynamic rational expectations theories to suggest that it might be useful and practical, while the implications for policy are different enough to be interesting.
Improved algorithms for optimal winner determination in combinatorial auctions and generalizations
, 2000
"... Combinatorial auctions can be used to reach efficient resource and task allocations in multiagent systems where the items are complementary. Determining the winners is NPcomplete and inapproximable, but it was recently shown that optimal search algorithms do very well on average. This paper present ..."
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Cited by 598 (55 self)
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Combinatorial auctions can be used to reach efficient resource and task allocations in multiagent systems where the items are complementary. Determining the winners is NPcomplete and inapproximable, but it was recently shown that optimal search algorithms do very well on average. This paper
KernelBased Object Tracking
, 2003
"... A new approach toward target representation and localization, the central component in visual tracking of nonrigid objects, is proposed. The feature histogram based target representations are regularized by spatial masking with an isotropic kernel. The masking induces spatiallysmooth similarity fu ..."
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Cited by 889 (4 self)
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functions suitable for gradientbased optimization, hence, the target localization problem can be formulated using the basin of attraction of the local maxima. We employ a metric derived from the Bhattacharyya coefficient as similarity measure, and use the mean shift procedure to perform the optimization
Modeling Rational Agents within a BDIArchitecture
, 1991
"... Intentions, an integral part of the mental state of an agent, play an important role in ..."
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Cited by 1032 (21 self)
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Intentions, an integral part of the mental state of an agent, play an important role in
Optimal Aggregation Algorithms for Middleware
 IN PODS
, 2001
"... Assume that each object in a database has m grades, or scores, one for each of m attributes. For example, an object can have a color grade, that tells how red it is, and a shape grade, that tells how round it is. For each attribute, there is a sorted list, which lists each object and its grade under ..."
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Cited by 701 (4 self)
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must access every object in the database, to find its grade under each attribute. Fagin has given an algorithm (“Fagin’s Algorithm”, or FA) that is much more efficient. For some monotone aggregation functions, FA is optimal with high probability in the worst case. We analyze an elegant and remarkably
Results 1  10
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