2014 Sixth International Symposium on Parallel Architectures, Algorithms and Programming (PAAP) (2014)

Beijing, China

July 13, 2014 to July 15, 2014

ISSN: 2168-3034

ISBN: 978-1-4799-3844-5

pp: 99-103

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/PAAP.2014.52

ABSTRACT

Let G = (V, E) be a given graph, S &sube; V be a terminalset, r &epsis; S be the selected root. Assume that c: E &rarr; &Ropf;+ and d: E &rarr; &Ropf;+ are cost and delay functionson the edges respectively. The shallow-light Steiner tree SLST) problem is to compute a minimum cost tree spanning all the terminalsof S, such that the delay between r and every other terminalis bounded by a given delay constraint D &epsis; &Ropf;0+. Since in real network, the cost and delay of a link are always related, this paper addresses two such special cases: the constrained Steinertree (CST) problem, a special case of the SLST problem that c(e)=&sigma; d(e) for every edge, and the constrained spanning tree (CPT) problem, afurther special case of the CST problem when S = V. This paper first shows that even when c(e) = d(e), the CPT problemis NP-hard, and admits no (1+ &epsi; &gamma; ln(|V|)-approximation algorithm for some fixed &gamma; > 0 and any &epsi; <.

INDEX TERMS

Approximation methods, Delays, Approximation algorithms, Steiner trees, Algorithm design and analysis, Silicon, Polynomials,inapproximability, Bifactor approximation algorithm, constrained Steiner tree, constrained spanning tree, NP-hardness

CITATION

Longkun Guo,
Nianchen Zou,
Yidong Li,
"Approximating the Shallow-Light Steiner Tree Problem When Cost and Delay are Linearly Dependent",

*2014 Sixth International Symposium on Parallel Architectures, Algorithms and Programming (PAAP)*, vol. 00, no. , pp. 99-103, 2014, doi:10.1109/PAAP.2014.52