An Oracle Strongly Polynomial Algorithm for Bottleneck Expansion Problems
Let E = { e 1 , e 2 , , e n } be a finite set and $\cal F $ be a family of subsets of E . For each element e i in E , c i is a given capacity and w i is the cost of increasing capacity c i by one unit. The problem is how to expand the capacities of elements in E so that the capacity of $\cal F $ is...
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| Vydáno v: | Optimization methods & software Ročník 17; číslo 1; s. 61 - 75 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Taylor & Francis Group
01.02.2002
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| Témata: | |
| ISSN: | 1055-6788, 1029-4937 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | Let E = { e 1 , e 2 , , e n } be a finite set and $\cal F $ be a family of subsets of E . For each element e i in E , c i is a given capacity and w i is the cost of increasing capacity c i by one unit. The problem is how to expand the capacities of elements in E so that the capacity of $\cal F $ is as large as possible, subject to a given budget restriction. This problem was introduced in [1] where an algorithm was proposed which is polynomial under some conditions. However, that method is not strongly polynomial. In this paper this problem is solved by solving a combinatorial equation. It is shown that if the problem $ \min _{F\in {\cal F}}w(F) $ is solvable in strongly polynomial time, then the bottleneck expansion problem is also solvable in strongly polynomial time. This result is stronger than what the method in [1] gives. In addition, some interesting variations of this problem are also discussed. |
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| ISSN: | 1055-6788 1029-4937 |
| DOI: | 10.1080/10556780290027819 |