### 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 language | English (US) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 92-105 |

Number of pages | 14 |

Volume | 3827 LNCS |

DOIs | |

State | Published - 2005 |

Event | 16th International Symposium on Algorithms and Computation, ISAAC 2005 - Hainan, China Duration: Dec 19 2005 → Dec 21 2005 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 3827 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 16th International Symposium on Algorithms and Computation, ISAAC 2005 |
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Country | China |

City | Hainan |

Period | 12/19/05 → 12/21/05 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - GEN-LARAC

T2 - A generalized approach to the constrained shortest path problem under multiple additive constraints

AU - Xiao, Ying

AU - Thulasiraman, Krishnaiyan

AU - Xue, Guoliang

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33744959285&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33744959285&partnerID=8YFLogxK

U2 - 10.1007/11602613_11

DO - 10.1007/11602613_11

M3 - Conference contribution

AN - SCOPUS:33744959285

SN - 3540309357

SN - 9783540309352

VL - 3827 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 92

EP - 105

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -