Weighted k ‐cardinality trees: Complexity and polyhedral structure

Weighted k ‐cardinality trees: Complexity and polyhedral structure We consider the k‐CARD TREE problem, i.e., the problem of finding in a given undirected graph G a subtree with k edges, having minimum weight. Applications of this problem arise in oil‐field leasing and facility layout. Although the general problem is shown to be strongly NP hard, it can be solved in polynomial time if G is itself a tree. We give an integer programming formulation of k‐CARD TREE and an efficient exact separation routine for a set of generalized subtour elimination constraints. The polyhedral structure of the convex hull of the integer solutions is studied. © 1994 by John Wiley & Sons, Inc. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Networks: An International Journal Wiley

Weighted k ‐cardinality trees: Complexity and polyhedral structure

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Publisher
Wiley
Copyright
Copyright © 1994 Wiley Periodicals, Inc., A Wiley Company
ISSN
0028-3045
eISSN
1097-0037
DOI
10.1002/net.3230240103
Publisher site
See Article on Publisher Site

Abstract

We consider the k‐CARD TREE problem, i.e., the problem of finding in a given undirected graph G a subtree with k edges, having minimum weight. Applications of this problem arise in oil‐field leasing and facility layout. Although the general problem is shown to be strongly NP hard, it can be solved in polynomial time if G is itself a tree. We give an integer programming formulation of k‐CARD TREE and an efficient exact separation routine for a set of generalized subtour elimination constraints. The polyhedral structure of the convex hull of the integer solutions is studied. © 1994 by John Wiley & Sons, Inc.

Journal

Networks: An International JournalWiley

Published: Jan 1, 1994

References

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