### Abstract

Consider a directed graph G(V; E), where V is the set of nodes and E is the set of links in G. Each link (u; v) is associated with a set of k C 1 additive nonnegative integer weights C_{uv} D (cuv;w^{1} uv;w^{2} _{uv}; : : : ;wk _{uv}). Here, c_{uv} is called the cost of link (u; v) and wi _{uv} is called the ith delay of (u; v). Given any two distinguish nodes s and t, the QoS routing (QSR) problem QSR(k) is to determine a minimum cost s-t path such that the ith delay on the path is atmost a specied bound. This problem is NP-complete. The LARAC algorithm based on a relaxation of the problem is a very efficient approximation algorithm for QSR(1). In this paper, we present a generalization of the LARAC algorithm called GEN-LARAC. A detailed convergence analysis of GEN-LARAC with simulation results is given. Simulation results provide an evidence of the excellent performance of GEN-LARAC.We also give a strongly polynomial time approximation algorithm for the QSR(1) problem.

Original language | English (US) |
---|---|

Article number | 7103034 |

Pages (from-to) | 242-251 |

Number of pages | 10 |

Journal | IEEE Transactions on Emerging Topics in Computing |

Volume | 4 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1 2016 |

### Fingerprint

### Keywords

- algorithms
- Combinatorial optimization
- Lagrangian relaxation,
- QoS routing

### ASJC Scopus subject areas

- Computer Science (miscellaneous)
- Computer Science Applications
- Human-Computer Interaction
- Information Systems

### Cite this

*IEEE Transactions on Emerging Topics in Computing*,

*4*(2), 242-251. [7103034]. https://doi.org/10.1109/TETC.2015.2428654

**QoS Routing under Multiple Additive Constraints : A Generalization of the LARAC Algorithm.** / Xiao, Ying; Thulasiraman, Krishnaiyan; Xue, Guoliang; Yadav, Mamta.

Research output: Contribution to journal › Article

*IEEE Transactions on Emerging Topics in Computing*, vol. 4, no. 2, 7103034, pp. 242-251. https://doi.org/10.1109/TETC.2015.2428654

}

TY - JOUR

T1 - QoS Routing under Multiple Additive Constraints

T2 - A Generalization of the LARAC Algorithm

AU - Xiao, Ying

AU - Thulasiraman, Krishnaiyan

AU - Xue, Guoliang

AU - Yadav, Mamta

PY - 2016/4/1

Y1 - 2016/4/1

N2 - Consider a directed graph G(V; E), where V is the set of nodes and E is the set of links in G. Each link (u; v) is associated with a set of k C 1 additive nonnegative integer weights Cuv D (cuv;w1 uv;w2 uv; : : : ;wk uv). Here, cuv is called the cost of link (u; v) and wi uv is called the ith delay of (u; v). Given any two distinguish nodes s and t, the QoS routing (QSR) problem QSR(k) is to determine a minimum cost s-t path such that the ith delay on the path is atmost a specied bound. This problem is NP-complete. The LARAC algorithm based on a relaxation of the problem is a very efficient approximation algorithm for QSR(1). In this paper, we present a generalization of the LARAC algorithm called GEN-LARAC. A detailed convergence analysis of GEN-LARAC with simulation results is given. Simulation results provide an evidence of the excellent performance of GEN-LARAC.We also give a strongly polynomial time approximation algorithm for the QSR(1) problem.

AB - Consider a directed graph G(V; E), where V is the set of nodes and E is the set of links in G. Each link (u; v) is associated with a set of k C 1 additive nonnegative integer weights Cuv D (cuv;w1 uv;w2 uv; : : : ;wk uv). Here, cuv is called the cost of link (u; v) and wi uv is called the ith delay of (u; v). Given any two distinguish nodes s and t, the QoS routing (QSR) problem QSR(k) is to determine a minimum cost s-t path such that the ith delay on the path is atmost a specied bound. This problem is NP-complete. The LARAC algorithm based on a relaxation of the problem is a very efficient approximation algorithm for QSR(1). In this paper, we present a generalization of the LARAC algorithm called GEN-LARAC. A detailed convergence analysis of GEN-LARAC with simulation results is given. Simulation results provide an evidence of the excellent performance of GEN-LARAC.We also give a strongly polynomial time approximation algorithm for the QSR(1) problem.

KW - algorithms

KW - Combinatorial optimization

KW - Lagrangian relaxation,

KW - QoS routing

UR - http://www.scopus.com/inward/record.url?scp=84976464804&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84976464804&partnerID=8YFLogxK

U2 - 10.1109/TETC.2015.2428654

DO - 10.1109/TETC.2015.2428654

M3 - Article

AN - SCOPUS:84976464804

VL - 4

SP - 242

EP - 251

JO - IEEE Transactions on Emerging Topics in Computing

JF - IEEE Transactions on Emerging Topics in Computing

SN - 2168-6750

IS - 2

M1 - 7103034

ER -