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- W2047251073 abstract "Let E be a finite set and F be a family of subsets of E. For each element e∊E, a weight w e is prescribed. Let be a given partition ofE. For any S∊F., let We consider the problem of minimizing g(S)over S∊f, and the problem of minimizing g(S) over those S∊F which satisfy f(S)D, wheref:F→RandD∊R. It is shown that if p is fixed, then both of these problems can be solved in polynomial time provided a related auxiliary problem can be solved in polynomial time. When p=O(|E|), it is shown that both theseproblems are NP-hard even when F is the base system of a simple class of partition matroids and we ’s are 0 or 1 only. We also suggest a method to compute a lower bound for the optimal objective function value. Finally, approximation algorithms for certain graph theoretic versions of these problems are discussed and shown to produce solutions with guaranteed error bound." @default.
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- W2047251073 date "1995-01-01" @default.
- W2047251073 modified "2023-09-24" @default.
- W2047251073 title "Generalized Bottleneck Problems∗" @default.
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- W2047251073 doi "https://doi.org/10.1080/02331939508844137" @default.
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