Journal ArticleDOI
Algorithms for Measuring Perturbability in Matroid Optimization
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An algorithm for computing the perturbability function of a matroid is presented that runs in strongly polynomial time for matroids in which independence can be tested in strongly Poole's inequality.Abstract:
of a matroid measures the maximum increase in the weight of its minimum weight bases that can be produced by increases of a given total cost on the weights of its elements. We present an algorithm for computing this function that runs in strongly polynomial time for matroids in which independence can be tested in strongly polynomial time. Furthermore, for the case of transversal matroids we are able to take advantage of their special structure to design a faster algorithm for computing the perturbability function.read more
Citations
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Journal ArticleDOI
Increasing the weight of minimum spanning trees
TL;DR: The problems of computing the maximum increase in the weight of the minimum spanning trees of a graph caused by the removal of a given number of edges, or by finite increases in the weights of the edges, are investigated.
Algorithms for Graphic Polymatroids and Parametric s-Sets ; CU-CS-736-94
TL;DR: These algorithms are based on a new characterization of the vectors in a graphic polymatroid, and also on an extension of parametric flow techniques to a problem concerning global minimum cuts, called parametric augmentation fors-sets.
Journal ArticleDOI
On Budgeted Optimization Problems
TL;DR: In this paper, the authors give a method for solving certain budgeted optimization problems in strongly polynomial time, which can be applied to several known budgeted problems, and in addition they show two new applications.
ReportDOI
Maximizing the Minimum Source-Sink Path Subject to a Budget Constraint: Another View of the Minimum Cost Flow Routine
TL;DR: Given a linear cost function for lengthening arcs, a technique is shown for maximizing, within a budget, the shortest source—sink path length in a graph.
References
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Book
Introduction to Operations Research
TL;DR: The Simplex Method duality theory and sensitivity analysis for linear programming has been studied extensively in the field of operations research as mentioned in this paper, including the application of queueing theory inventory theory forecasting Markovian decision processes and applications decision analysis simulation.
Submodular functions, matroids, and certain polyhedra
TL;DR: The viewpoint of the subject of matroids, and related areas of lattice theory, has always been abstraction of algebraic dependence or, equivalently, abstraction of the incidence relations in geometric representations of algebra.
Journal ArticleDOI
A fast parametric maximum flow algorithm and applications
TL;DR: It is shown that the recent maximum flow algorithm of Goldberg and Tarjan can be extended to solve an important class of such parametric maximum flow problems, at the cost of only a constant factor in its worst-case time bound.
Journal ArticleDOI
Optimal attack and reinforcement of a network
TL;DR: Efficient algorithms for the optimal attack problem, the problem of computing the strength, and the problems of finding a minimum cost “reinforcement” to achieve a desired strength are given.