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 |
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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
Constrained shortest link-disjoint paths selection : A network programming based approach. / Xiao, Ying; Thulasiraman, Krishnaiyan; Xue, Guoliang.
In: IEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 53, No. 5, 05.2006, p. 1174-1187.Research output: Contribution to journal › Article
}
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 -