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Greedy and Optimal Paths in a Weighted Graph Without Circuits and Applications to a Class of Optimization Problems on Finite Posets

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Greedy and Optimal Paths in a Weighted Graph Without Circuits and Applications to a Class of Optimization Problems on Finite Posets

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dc.contributor.author Dragan, Irinel C. en
dc.date.accessioned 2010-06-02T21:08:10Z en
dc.date.available 2010-06-02T21:08:10Z en
dc.date.issued 1983-05 en
dc.identifier.uri http://hdl.handle.net/10106/2268 en
dc.description.abstract In several recent papers B. Korte and L. Lovasz considered a mathematical structure called a simple language on which a greedy algorithm can operate (see [31,J41, OD. The concept of greedoid has been defined by relaxing an axiom and strengthening an other axiom from the definition of the matroid. Under some constraints imposed to the objective function of a combinatorial optimization problem on a greedoid, the greedy algorithm provides an efficient method for solving the problem. An algorithmic characterization of the greedoids, similar to that of the matroids, was further searched. The effort has been justified-by several examples of combinatorial optimization problems defined on greedoids. A class of greedoids connected to finite posets has been also considered by U. Faigle (see 121). In this paper we consider a class of simple languages called the nonextendible languages without circuits and we examine the combinatorial optimization problems on such a language, under the Korte-Lovasz constraints imposed to the objective functions. The main result is that a greedy algorithm works for all such objective functions if and only if the non extendible language without circuits is a greedoid. The structure of these greedoids is clarified by means of the graph associated to a simple language, which has in this case particular properties. The problem of giving an algorithmic characterization of the greedoids underlined by extendible languages or non extendible languages with circuits is still an open question. The application of the results to a simple language defined on a finite poset is also discussed. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;197 en
dc.subject Greedy algorithm en
dc.subject Simple language en
dc.subject Greedoid en
dc.subject Korte-Lovasz constraints en
dc.subject Nonextendible languages without circuits en
dc.subject.lcsh Algorithms en
dc.subject.lcsh Mathematics Research en
dc.title Greedy and Optimal Paths in a Weighted Graph Without Circuits and Applications to a Class of Optimization Problems on Finite Posets en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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