### Abstract

Given a graph G with each link in the graph associated with two positive weights, cost and delay, we consider the problem of selecting a set f k link-disjoint paths from a node s to another node t such that the total cost of these paths is minimum and that the total delay of these paths is not greater than a specified bound. This problem, to be called the constrained shortest link-disjoint path (CSDP(k)) problem, can be formulated as an integer linear programming (ILP) problem. Relaxing the integrality constraints results in an upper bounded linear programming problem. We first show that the integer relaxations of the CSDP(k) problem and a generalized version of this problem to be called the generalized CSDP (GCSDP (k)) problem (in which each path is required to satisfy a specified bound on its delay) both have the same optimal objective value. In view of this, we focus our work on the relaxed form of the CSDP (k) problem (RELAX-CSDP(k)). We study RELAX-CSDP(k) from the primal perspective using the revised simplex method of linear programming. We discuss different issues such as formulas to identify entering and leaving variables, anti-cycling strategy, computational time complexity etc., related to an efficient implementation of our approach. We show how to extract from an optimal solution to RELAX-CSDP(k) a set of k link-disjoint s-t paths which is an approximate solution to the original CSDP(k) problem. We also derive bounds on the quality of this solution with respect to the optimum. We present simulation results that demonstrate that our algorithm is faster than currently available approaches. Our simulation results also indicate that in most cases the individual delays of the paths produced starting from RELAX-CSDP(k) do not deviate in a significant way from the individual path delay requirements of the GCSDP(k) problem.

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

Pages (from-to) | 1174-1187 |

Number of pages | 14 |

Journal | IEEE Transactions on Circuits and Systems I: Regular Papers |

Volume | 53 |

Issue number | 5 |

DOIs | |

State | Published - May 2006 |

### Fingerprint

### Keywords

- Combinatorial optimization
- Constrained shortest paths (CSP)
- Graph theory
- Linear programming
- Link-disjoint paths
- Network optimization
- QoS routing

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*IEEE Transactions on Circuits and Systems I: Regular Papers*,

*53*(5), 1174-1187. https://doi.org/10.1109/TCSI.2006.869907

**Constrained shortest link-disjoint paths selection : A network programming based approach.** / Xiao, Ying; Thulasiraman, Krishnaiyan; Xue, Guoliang.

Research output: Contribution to journal › Article

*IEEE Transactions on Circuits and Systems I: Regular Papers*, vol. 53, no. 5, pp. 1174-1187. https://doi.org/10.1109/TCSI.2006.869907

}

TY - JOUR

T1 - Constrained shortest link-disjoint paths selection

T2 - A network programming based approach

AU - Xiao, Ying

AU - Thulasiraman, Krishnaiyan

AU - Xue, Guoliang

PY - 2006/5

Y1 - 2006/5

N2 - Given a graph G with each link in the graph associated with two positive weights, cost and delay, we consider the problem of selecting a set f k link-disjoint paths from a node s to another node t such that the total cost of these paths is minimum and that the total delay of these paths is not greater than a specified bound. This problem, to be called the constrained shortest link-disjoint path (CSDP(k)) problem, can be formulated as an integer linear programming (ILP) problem. Relaxing the integrality constraints results in an upper bounded linear programming problem. We first show that the integer relaxations of the CSDP(k) problem and a generalized version of this problem to be called the generalized CSDP (GCSDP (k)) problem (in which each path is required to satisfy a specified bound on its delay) both have the same optimal objective value. In view of this, we focus our work on the relaxed form of the CSDP (k) problem (RELAX-CSDP(k)). We study RELAX-CSDP(k) from the primal perspective using the revised simplex method of linear programming. We discuss different issues such as formulas to identify entering and leaving variables, anti-cycling strategy, computational time complexity etc., related to an efficient implementation of our approach. We show how to extract from an optimal solution to RELAX-CSDP(k) a set of k link-disjoint s-t paths which is an approximate solution to the original CSDP(k) problem. We also derive bounds on the quality of this solution with respect to the optimum. We present simulation results that demonstrate that our algorithm is faster than currently available approaches. Our simulation results also indicate that in most cases the individual delays of the paths produced starting from RELAX-CSDP(k) do not deviate in a significant way from the individual path delay requirements of the GCSDP(k) problem.

AB - Given a graph G with each link in the graph associated with two positive weights, cost and delay, we consider the problem of selecting a set f k link-disjoint paths from a node s to another node t such that the total cost of these paths is minimum and that the total delay of these paths is not greater than a specified bound. This problem, to be called the constrained shortest link-disjoint path (CSDP(k)) problem, can be formulated as an integer linear programming (ILP) problem. Relaxing the integrality constraints results in an upper bounded linear programming problem. We first show that the integer relaxations of the CSDP(k) problem and a generalized version of this problem to be called the generalized CSDP (GCSDP (k)) problem (in which each path is required to satisfy a specified bound on its delay) both have the same optimal objective value. In view of this, we focus our work on the relaxed form of the CSDP (k) problem (RELAX-CSDP(k)). We study RELAX-CSDP(k) from the primal perspective using the revised simplex method of linear programming. We discuss different issues such as formulas to identify entering and leaving variables, anti-cycling strategy, computational time complexity etc., related to an efficient implementation of our approach. We show how to extract from an optimal solution to RELAX-CSDP(k) a set of k link-disjoint s-t paths which is an approximate solution to the original CSDP(k) problem. We also derive bounds on the quality of this solution with respect to the optimum. We present simulation results that demonstrate that our algorithm is faster than currently available approaches. Our simulation results also indicate that in most cases the individual delays of the paths produced starting from RELAX-CSDP(k) do not deviate in a significant way from the individual path delay requirements of the GCSDP(k) problem.

KW - Combinatorial optimization

KW - Constrained shortest paths (CSP)

KW - Graph theory

KW - Linear programming

KW - Link-disjoint paths

KW - Network optimization

KW - QoS routing

UR - http://www.scopus.com/inward/record.url?scp=33646506349&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646506349&partnerID=8YFLogxK

U2 - 10.1109/TCSI.2006.869907

DO - 10.1109/TCSI.2006.869907

M3 - Article

VL - 53

SP - 1174

EP - 1187

JO - IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

JF - IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

SN - 1549-8328

IS - 5

ER -