By Topic

On the complexity of and algorithms for finding the shortest path with a disjoint counterpart

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

5 Author(s)
Dahai Xu ; Dept. of Comput. Sci. & Eng., State Univ. of New York, USA ; Yang Chen ; Yizhi Xiong ; Chunming Qiao
more authors

Finding a disjoint path pair is an important component in survivable networks. Since the traffic is carried on the active (working) path most of the time, it is useful to find a disjoint path pair such that the length of the shorter path (to be used as the active path) is minimized. In this paper, we first address such a Min-Min problem. We prove that this problem is NP-complete in either single link cost (e.g., dedicated backup bandwidth) or dual link cost (e.g., shared backup bandwidth) networks. In addition, it is NP-hard to obtain a K-approximation to the optimal solution for any K>1. Our proof is extended to another open question regarding the computational complexity of a restricted version of the Min-Sum problem in an undirected network with ordered dual cost links (called the MSOD problem). To solve the Min-Min problem efficiently, we introduce a novel concept called conflicting link set which provides insights into the so-called trap problem, and develop a divide-and-conquer strategy. The result is an effective heuristic for the Min-Min problem called COnflicting Link Exclusion (COLE), which can outperform other approaches in terms of both the optimality and running time. We also apply COLE to the MSOD problem to efficiently provide shared path protection and conduct comprehensive performance evaluation as well as comparison of various schemes for shared path protection. We show that COLE not only processes connection requests much faster than existing integer linear programming (ILP)-based approaches but also achieves a good balance among the active path length, bandwidth efficiency, and recovery time.

Published in:

IEEE/ACM Transactions on Networking  (Volume:14 ,  Issue: 1 )