ISSN:
1436-4646
Keywords:
Polyhedral combinatorics
;
Packing subtrees
;
Knapsacks with precedence
;
Column generation
;
Dynamic programming
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract Given a treeG = (V, E) and a weight function defined on subsets of its nodes, we consider two associated problems. The first, called the “rooted subtree problem”, is to find a maximum weight subtree, with a specified root, from a given set of subtrees. The second problem, called “the subtree packing problem”, is to find a maximum weight packing of node disjoint subtrees chosen from a given set of subtrees, where the value of each subtree may depend on its root. We show that the complexity status of both problems is related, and that the subtree packing problem is polynomial if and only if each rooted subtree problem is polynomial. In addition we show that the convex hulls of the feasible solutions to both problems are related: the convex hull of solutions to the packing problem is given by “pasting together” the convex hulls of the rooted subtree problems. We examine in detail the case where the set of feasible subtrees rooted at nodei consists of all subtrees with at mostk nodes. For this case we derive valid inequalities, and specify the convex hull whenk ⩽ 4.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01585993
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