GEN-LARAC

A generalized approach to the constrained shortest path problem under multiple additive constraints

Ying Xiao, Krishnaiyan Thulasiraman, Guoliang Xue

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Citations (Scopus)

Abstract

Given a network modeled as a graph G with each link associated with a cost and k weights, the Constrained Shortest Path (CSP(k)) problem asks for computing a minimum cost path from a source node s to a target node t satisfying pre-specified bounds on path weights: This problem is NP-hard. In this paper we propose a new approximation algorithm called GEN-LARAC for CSP(k) problem based on Lagrangian relaxation method. For k = 1, we show that the relaxed problem can be solved by a polynomial time algorithm with time complexity O((m + n log n)2). Using this algorithm as a building block and combing it with ideas from mathematical programming, we propose an efficient algorithm for arbitrary k. We, prove the convergence of our algorithm and compare it with previously known algorithms. We point out that our algorithm is also applicable to a more general class of constrained optimization problems.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages92-105
Number of pages14
Volume3827 LNCS
DOIs
StatePublished - 2005
Event16th International Symposium on Algorithms and Computation, ISAAC 2005 - Hainan, China
Duration: Dec 19 2005Dec 21 2005

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3827 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other16th International Symposium on Algorithms and Computation, ISAAC 2005
CountryChina
CityHainan
Period12/19/0512/21/05

Fingerprint

Shortest Path Problem
Convergence of Algorithms
Path
Lagrangian Method
Lagrangian Relaxation
Relaxation Method
Costs
Constrained Optimization Problem
Vertex of a graph
Mathematical Programming
Shortest path
Building Blocks
Polynomial-time Algorithm
Time Complexity
Approximation Algorithms
Efficient Algorithms
NP-complete problem
Mathematical programming
Weights and Measures
Costs and Cost Analysis

ASJC Scopus subject areas

  • Computer Science(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Theoretical Computer Science

Cite this

Xiao, Y., Thulasiraman, K., & Xue, G. (2005). GEN-LARAC: A generalized approach to the constrained shortest path problem under multiple additive constraints. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3827 LNCS, pp. 92-105). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3827 LNCS). https://doi.org/10.1007/11602613_11

GEN-LARAC : A generalized approach to the constrained shortest path problem under multiple additive constraints. / Xiao, Ying; Thulasiraman, Krishnaiyan; Xue, Guoliang.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 3827 LNCS 2005. p. 92-105 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3827 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Xiao, Y, Thulasiraman, K & Xue, G 2005, GEN-LARAC: A generalized approach to the constrained shortest path problem under multiple additive constraints. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 3827 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3827 LNCS, pp. 92-105, 16th International Symposium on Algorithms and Computation, ISAAC 2005, Hainan, China, 12/19/05. https://doi.org/10.1007/11602613_11
Xiao Y, Thulasiraman K, Xue G. GEN-LARAC: A generalized approach to the constrained shortest path problem under multiple additive constraints. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 3827 LNCS. 2005. p. 92-105. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/11602613_11
Xiao, Ying ; Thulasiraman, Krishnaiyan ; Xue, Guoliang. / GEN-LARAC : A generalized approach to the constrained shortest path problem under multiple additive constraints. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 3827 LNCS 2005. pp. 92-105 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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