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author:

Guo, Longkun (Guo, Longkun.) [1] (Scholars:郭龙坤) | Shen, Hong (Shen, Hong.) [2] | Liao, Kewen (Liao, Kewen.) [3]

Indexed by:

EI Scopus SCIE

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 + beta, max{2, 1 + ln(1/ beta)}) 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 beta = 0, the algorithm is shown to be with ratio (1, O(ln n)), i.e. it is an algorithm with only a single factor ratio O(ln n) 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.

Keyword:

Auxiliary graph Bifactor approximation algorithm Cycle cancellation k-disjoint bi-constraint path NP-hard

Community:

  • [ 1 ] [Guo, Longkun]Fuzhou Univ, Sch Math & Comp Sci, Fuzhou 350002, Peoples R China
  • [ 2 ] [Shen, Hong]Univ Adelaide, Sch Comp Sci, Adelaide, SA, Australia
  • [ 3 ] [Liao, Kewen]Univ Adelaide, Sch Comp Sci, Adelaide, SA, Australia

Reprint 's Address:

  • 郭龙坤

    [Guo, Longkun]Fuzhou Univ, Sch Math & Comp Sci, Fuzhou 350002, Peoples R China

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Source :

JOURNAL OF COMBINATORIAL OPTIMIZATION

ISSN: 1382-6905

Year: 2015

Issue: 1

Volume: 29

Page: 153-164

1 . 0 8

JCR@2015

0 . 9 0 0

JCR@2023

ESI Discipline: MATHEMATICS;

ESI HC Threshold:86

JCR Journal Grade:2

CAS Journal Grade:3

Cited Count:

WoS CC Cited Count:

SCOPUS Cited Count: 6

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 0

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