## Efficient Algorithms for Robustness in Matroid Optimization (1996)

Venue: | PROCEEDINGS OF THE EIGHTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS (NEW |

Citations: | 8 - 1 self |

### BibTeX

@INPROCEEDINGS{Frederickson96efficientalgorithms,

author = {Greg N. Frederickson and Roberto Solis-Oba},

title = {Efficient Algorithms for Robustness in Matroid Optimization},

booktitle = {PROCEEDINGS OF THE EIGHTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS (NEW},

year = {1996},

pages = {659--668},

publisher = {}

}

### Years of Citing Articles

### OpenURL

### Abstract

The robustness function 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. We identify key properties of transversal, scheduling and partition matroids, and exploit them to design robustness algorithms that are more efficient than our general algorithm.

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Citation Context ...or B=w k [ D k , and thus, a maximum flow for G. We assume that the largest deadline among the jobs in D k [ B=w k is at most jD k [ B=w k j. If this condition does not hold, we use the techniques in =-=[10]-=- to modify, in O(jD k [ B=w k j) time, the deadlines so that this condition is satisfied. The extra time required by this step does not affect the overall time complexity of our algorithm. A straightf... |

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Citation Context ...he robustness function, but evaluates the robustness function only at a required point, and does so in O(m) time. This formulation is a version of the optimal distribution of effort problem (see e.g. =-=[22]-=-). Since we do not have explicit representations for the gain functions, we cannot use any of the known methods of solution for the latter problem [9, 22]. Instead, we present a new approach that opti... |

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Citation Context ...computed in O(m 4 i n i +m 3 i n 3 i ) time, where m i = jE i j andsis the time required to test whether a set of at most n i elements is independent in M i . Proof. We use the algorithm by Narayanan =-=[27]-=- to solve problem (1) in O(m 4 i +m 3 i n 2 i ) time. Since we have to solve at most n i problems of the form (1) to find a set of smallest rate in M i , the total time needed to solve the problem is ... |

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Citation Context ... that are more efficient than our general algorithm. 1 Introduction A fundamental problem in the study of dynamic systems is that of measuring how sensitive a problem is to perturbations in its input =-=[19, 26]-=-. A significant limitation of the current methods for sensitivity analysis in combinatorial optimization is that they measure only changes in the solution of a problem produced by perturbations in the... |