The Polymatroid Steiner Problems

G. Calinescu () and A. Zelikovsky ()
Additional contact information
G. Calinescu: Illinois Institute of Technology
A. Zelikovsky: Georgia State University

Journal of Combinatorial Optimization, 2005, vol. 9, issue 3, No 4, 294 pages

Abstract: Abstract The Steiner tree problem asks for a minimum cost tree spanning a given set of terminals S⊂eqV in a weighted graph G = (V,E,c), c:E→ R+. In this paper we consider a generalization of the Steiner tree problem, so called Polymatroid Steiner Problem, in which a polymatroid P = P(V) is defined on V and the Steiner tree is required to span at least one base of P (in particular, there may be a single base S⊂eqV). This formulation is motivated by the following application in sensor networks – given a set of sensors S = {s1,…,s k }, each sensor s i can choose to monitor only a single target from a subset of targets X i , find minimum cost tree spanning a set of sensors capable of monitoring the set of all targets X = X1 ∪ … ∪ X k . The Polymatroid Steiner Problem generalizes many known Steiner tree problem formulations including the group and covering Steiner tree problems. We show that this problem can be solved with the polylogarithmic approximation ratio by a generalization of the combinatorial algorithm of Chekuri et al. (2002). We also define the Polymatroid directed Steiner problem which asks for a minimum cost arborescence connecting a given root to a base of a polymatroid P defined on the terminal set S. We show that this problem can be approximately solved by algorithms generalizing methods of Chekuri et al. (2002).

Keywords: wireless sensor networks; Steiner trees; polymatroid; approximation algorithms (search for similar items in EconPapers)
Date: 2005
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10878-005-1412-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:9:y:2005:i:3:d:10.1007_s10878-005-1412-9

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-005-1412-9

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().