1. Algorithm for enumerating all recovery paths against single span of a network Sung-Hwan Park (ozjezz@icu.ac.kr)ozjezz@icu.ac.kr Jeong-Hee Ryou (viva02@icu.ac.kr)viva02@icu.ac.kr ICE514 Term Project 2003. 4. 14

2. 2 ICE 514 Concrete Mathematics 광주대학교 컴퓨터 학과 RSVP 및 실시간 인터넷 서비스 기술 2  Introduction  Related works  Algorithm  References Contents

3. 3 ICE 514 Concrete Mathematics 광주대학교 컴퓨터 학과 RSVP 및 실시간 인터넷 서비스 기술 3 I. Introduction  Motivation  Rapid growth in popularity of internet, data network More higher capacity of a link  Critical problem Span fail can potentially lead to the loss of a large amount of data  Importance of recovery scheme Develop appropriate recovery schemes which minimize the data loss when a span failure occurs Rerouting around failure on an alternate path

4. 4 ICE 514 Concrete Mathematics 광주대학교 컴퓨터 학과 RSVP 및 실시간 인터넷 서비스 기술 4 I. Introduction  Objective  For constructing data base of recovery routes Search for all eligible recovery routes.  For extension of proposal scheme Resource minimization : reduce the total number of transmission systems required to carry both the working and the spare capacity

5. 5 ICE 514 Concrete Mathematics 광주대학교 컴퓨터 학과 RSVP 및 실시간 인터넷 서비스 기술 5 II. Related works  Graph Theory  The information of a graph are stated in matrix form.  Associated matrics Adjacency matrix, incidence matrix, distance matrix,…..  Incidence matrix  Both nodes and edges in a graph are labeled. Let the nodes of graph G be labeled v 1, v 2,….. v p and the edges be labeled e 1, e 2,….. e q. The incidence matrix B of G is the p x q binary matrix b ij = 1 if v i is incident with e j 0otherwise. {

6. 6 ICE 514 Concrete Mathematics 광주대학교 컴퓨터 학과 RSVP 및 실시간 인터넷 서비스 기술 6 III. Implementation of Algorithm  Algorithm  Matrix Node = node in network Edge = link between nodes in network  Results Enumerate all available routes for certain source and destination node.  Implementation environment  VC++

7. 7 ICE 514 Concrete Mathematics 광주대학교 컴퓨터 학과 RSVP 및 실시간 인터넷 서비스 기술 7 III. Implementation of Algorithm  Sample network  Matrix B [no_nodes][no_links]= 0 1 4 2 3 0 1 4 2 5 63 7 0 1 2 3 4 5 6 7 0 1 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 0 2 0 0 1 0 0 1 1 0 3 0 0 0 1 0 1 0 1 4 0 1 0 0 1 0 1 1

8. 8 ICE 514 Concrete Mathematics 광주대학교 컴퓨터 학과 RSVP 및 실시간 인터넷 서비스 기술 8 III. Implementation of Algorithm 1 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 1 0 1 0 0 1 0 1 1 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 1 1 0,10,4,1 0,4,2,1 S:0, D:1

9. 9 ICE 514 Concrete Mathematics 광주대학교 컴퓨터 학과 RSVP 및 실시간 인터넷 서비스 기술 9 III. Implementation of Algorithm  Result  Source : 0, Destination : 1  available routes 0 1 0 4 1 0 4 2 1 0 4 2 3 1 0 4 3 1 0 4 3 2 1

10. 10 ICE 514 Concrete Mathematics 광주대학교 컴퓨터 학과 RSVP 및 실시간 인터넷 서비스 기술 10 IV. References [1] Meir Herzberg and Stephen J.Bye, “An Optimal Spare-Capacity Assignment Model for Survivable Networks with Hop Limits” IEEE 1994. [2] Fred Buckley and Frank Harary, “Distance in Graphs” 1990. [3] Douglas B.West, “Introduction to Graph Theory” 2001. [4] P. Mateti and N. Deo, "On algorithms for enumerating all circuits of a graph," SIAM J. Comput., Vol. 5, No. 1, Mar. 1976, pp. 90-99. [5] M. H. MacGregor and W. D. Grover, "Optimized k-shortest-paths Algorithm for Facility Restoration," Software - Practice and Experience, Vol. 24, No. 9, pp. 823-834.