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
ABSTRACT
Let G = (V, E) be a given graph, S &amp;sube; V be a terminalset, r &amp;epsis; S be the selected root. Assume that c: E &amp;rarr; &amp;Ropf;+ and d: E &amp;rarr; &amp;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 &amp;epsis; &amp;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)=&amp;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+ &amp;epsi; &amp;gamma; ln(|V|)-approximation algorithm for some fixed &amp;gamma; > 0 and any &amp;epsi; <.
INDEX TERMS
Approximation methods, Delays, Approximation algorithms, Steiner trees, Algorithm design and analysis, Silicon, Polynomials
CITATION

L. Guo, N. Zou and Y. 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), Beijing, China, 2014, pp. 99-103.
doi:10.1109/PAAP.2014.52