On Finding Disjoint Paths in Single and Dual Link Cost Networks

1. On Finding Disjoint Pathsin Single and Dual Link Cost Networks Chunming Qiao* LANDER, CSE Department SUNY at Buffalo *Collaborators: Dahai Xu, Yang Chen, Yizhi Xiong and Xin He Good afternoon, Thanks for attending. I am Dahai Xu, I am happy to have this chance to introduce our work on Survivable Routing.Good afternoon, Thanks for attending. I am Dahai Xu, I am happy to have this chance to introduce our work on Survivable Routing.

2. Outline The Min-Min Problem Motivation and Definition Existing and Proposed Heuristics Application and Performance Evaluation Summary Introduce... Present, our contributions, particularly, focus on one aspect of our research, discuss Finally, I will summarize my talk and propose my future research plans #Performance EvaluationIntroduce... Present, our contributions, particularly, focus on one aspect of our research, discuss Finally, I will summarize my talk and propose my future research plans #Performance Evaluation

3. Finding Disjoint Path Pairs Basic and important problem in survivable routing The Min-Min Problem Definition: Finding a link (node) disjoint path pair such that the length of the shorter path is minimized. Applications Encrypted data on the shorter path, and decryption key on the longer path Shared Path Protection (use the shorter path as AP) Counterpart problems Min-Max Min-Sum A short BP and thus a fast recovery time.A short BP and thus a fast recovery time.

4. Computational Complexities Min-Sum (P) [Suurballe-74] Min-Max (NP Complete) [Li-90] Min-Min (P or NP Hard?) NP Complete! proved by Xu et. al. in INFOCOM�04] Reduction from a well-known NPC problem 3SAT We also proved that it is NP-hard to obtain a k-approximation to the optimal solution for any k > 1 Now we will discuss the Computational Complexities for the three related problems. Polynomial time resolvable. But the Computational Complexity of Min-Min is still an open question The proof is the.. It means it will be very difficult to design a heuristic algorithm to achieve near optimal result. Chung-Lun Li, Satisfiability Shared Min-Sum (NP Complete) [Liu-02] Now we will discuss the Computational Complexities for the three related problems. Polynomial time resolvable. But the Computational Complexity of Min-Min is still an open question The proof is the.. It means it will be very difficult to design a heuristic algorithm to achieve near optimal result. Chung-Lun Li, Satisfiability Shared Min-Sum (NP Complete) [Liu-02]

5. Solving The Min-Min Problem Active Path First (APF) Heuristic Finds a shortest path for use as AP, followed by searching a disjoint BP. It may fail to find such a BP even though a disjoint path pair does exist. K Shortest Path (KSP) Heuristic First K shortest paths are found and tested in the increasing order of their costs (path lengths) to see if a disjoint BP exists. Could be time-consuming There are two existing heuristics to solve Min-Min. The first is APF where we try to find a shortest path to be used as AP. Then we will remove the links along the AP temporarily, and find BP in the rest network. Because the APs are searched in a brute-force way solely based on their path lengths.There are two existing heuristics to solve Min-Min. The first is APF where we try to find a shortest path to be used as AP. Then we will remove the links along the AP temporarily, and find BP in the rest network. Because the APs are searched in a brute-force way solely based on their path lengths.

6. Inefficiency of KSP Any path from s to d consists of two sub-paths in domain E1 and E2 respectively. Links in E1 is much shorter than those in E2. The number of all possible sub-paths in E1 is very large