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)ove...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.Read More
Publication Year: 1995
Publication Date: 1995-01-01
Language: en
Type: article
Indexed In: ['crossref']
Access and Citation
Cited By Count: 7
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