Improved approximation algorithms for computing k disjoint paths subject to two constraints

Journal article


Guo, Longkun, Shen, Hong and Liao, Kewen. (2015). Improved approximation algorithms for computing k disjoint paths subject to two constraints. Journal of Combinatorial Optimization. 29(1), pp. 153-164. https://doi.org/10.1007/s10878-013-9693-x
AuthorsGuo, Longkun, Shen, Hong and Liao, Kewen
Abstract

For a given graph G with distinct vertices s and t, nonnegative integral cost and delay on edges, and positive integral bound C and D on cost and delay respectively, the k bi-constraint path (kBCP) problem is to compute k disjoint st-paths subject to C and D. This problem is known to be NP-hard, even when k=1 (Garey and Johnson, Computers and Intractability, 1979). 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+ln(1/β)}) 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 immediately and a factor-(1.567,1.567) algorithm by slightly modifying the algorithm. Besides, when β=0, the algorithm is shown to be with ratio (1,O(lnn)), i.e. it is an algorithm with only a single factor ratio O(lnn) on cost. To the best of our knowledge, this is the first non-trivial approximation algorithm that strictly obeys the delay constraint for the kBCP problem.

Keywordsk-disjoint bi-constraint path; NP-hard; bifactor approximation algorithm; auxiliary graph; cycle cancellation
Year2015
JournalJournal of Combinatorial Optimization
Journal citation29 (1), pp. 153-164
PublisherSpringer
ISSN1382-6905
Digital Object Identifier (DOI)https://doi.org/10.1007/s10878-013-9693-x
Scopus EID2-s2.0-84920707889
Research or scholarlyResearch
Page range153-164
Publisher's version
License
All rights reserved
File Access Level
Controlled
Output statusPublished
Publication dates
Print06 Dec 2013
Publication process dates
Deposited09 Aug 2021
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