Abstract
Consider a communication network G in which a limited number of link and/or node faults F might occur. A routing p for the network (a fixed path between each pair of nodes) must be chosen without any knowledge of which components might become faulty. Choosing a good routing corresponds to bounding the diameter of the surviving route graph R(G,ρ)/F, where two nonfaulty nodes are joined by an edge if there are no faults on the route between them. We prove a number of results concerning the diameter of surviving route graphs. We show that if p is a minimal length routing, then the diameter of R(G, ρ)/F can be on the order of the number of nodes of G, even if F consists of only a single node. However, if G is the n-dimensional cube, the diameter of R(G, ρ)/F<3 for any minimal length routing p and any set of faults F with IFl<n. We also show that if F consists only of edges and does not disconnect G, then the diameter of R(G, ρ)/F is < 3IFI+1, while if F consists only of nodes and does not disconnect G, then the diameter of R(G, ρ)/F is < the sum of the degrees of the nodes in F, where in both cases ρ is an arbitrary minimal length routing. We conclude with one of the most important contributions of this paper: a list of interesting and apparently difficult open problems.
Original language | English |
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Title of host publication | Proceedings of the 16th Annual ACM Symposium on Theory of Computing, STOC 1984 |
Publisher | Association for Computing Machinery |
Pages | 526-535 |
Number of pages | 10 |
ISBN (Electronic) | 0897911334 |
DOIs | |
State | Published - 1 Dec 1984 |
Event | 16th Annual ACM Symposium on Theory of Computing, STOC 1984 - Washington, United States Duration: 30 Apr 1984 → 2 May 1984 |
Publication series
Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
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ISSN (Print) | 0737-8017 |
Conference
Conference | 16th Annual ACM Symposium on Theory of Computing, STOC 1984 |
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Country/Territory | United States |
City | Washington |
Period | 30/04/84 → 2/05/84 |
Bibliographical note
Publisher Copyright:© 1984 ACM.