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Type: Conference paper
Title: Improved approximation algorithms for computing k disjoint paths subject to two constraints
Author: Guo, L.
Shen, H.
Liao, K.
Citation: Proceedings of the 19th International Computing and Combinatorics Conference, COCOON 2013, 2013, Hangzhou, China, June 21-23, 2013 / D.-Z. Du, G. Zhang (eds.), pp.325-336
Publisher: Springer
Publisher Place: Germany
Issue Date: 2013
Series/Report no.: Lecture Notes in Computer Science
ISBN: 9783642387678
ISSN: 0302-9743
Conference Name: International Computing and Combinatorics Conference (19th : 2013 : Hangzhou)
Statement of
Longkun Guo, Hong Shen, and Kewen Liao
Abstract: For a given graph G with positive integral cost and delay on edges, distinct vertices s and t, cost bound C ∈ Z  +  and delay bound D ∈ Z  + , the k bi-constraint path (kBCP) problem is to compute k disjoint st-paths subject to C and D. This problem is known NP-hard, even when k = 1 [4]. This paper first gives a simple approximation algorithm with factor-(2,2), i.e. the algorithm computes a solution with delay and cost bounded by 2*D and 2*C respectively. Later, a novel improved approximation algorithm with ratio (1+β,max{2,1+ln1β}) is developed by constructing interesting auxiliary graphs and employing the cycle cancellation method. As a consequence, we can obtain a factor-(1.369, 2) approximation algorithm by setting 1+ln1β=2 and a factor-(1.567, 1.567) algorithm by setting 1+β=1+ln1β . Besides, by setting β = 0, an approximation algorithm with ratio (1, O(ln n)), i.e. an algorithm with only a single factor ratio O(ln n) on cost, can be immediately obtained. To the best of our knowledge, this is the first non-trivial approximation algorithm for the kBCP problem that strictly obeys the delay constraint.
Keywords: k-disjoint bi-constraint path
bifactor approximation algorithm
auxiliary graph
cycle cancellation
Rights: © Springer-Verlag Berlin Heidelberg 2013
DOI: 10.1007/978-3-642-38768-5_30
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