Fault tolerance of minimal path routings in a network
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
A new look at fault-tolerant network routing
Information and Computation
On fault tolerant routings in general networks
Information and Computation
Efficient fault—tolerant routings in networks
Information and Computation
Fault-tolerant routings in a &kgr;-connected network
Information Processing Letters
Efficient fault-tolerant fixed routings on (k+1)-connected digraphs
Discrete Applied Mathematics - Special double volume: interconnection networks
Optimal fault-tolerant routings for connected graphs
Information Processing Letters
Information and Computation
Graph Algorithms
A Scalable Approach to Routing in ATM Networks
WDAG '94 Proceedings of the 8th International Workshop on Distributed Algorithms
Optimal Fault-Tolerant ATM-Routings for Biconnected Graphs
WG '97 Proceedings of the 23rd International Workshop on Graph-Theoretic Concepts in Computer Science
Extremal Graph Theory
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We study the problem of designing fault-tolerant routings with small routing tables for a k-connected network of n processors in the surviving route graph model. The surviving route graph R(G, ρ)/F for a graph G, a routing ρ and a set of faults F is a directed graph consisting of nonfaulty nodes with a directed edge from a node x to a node y iff there are no faults on the route from x to y. The diameter of the surviving route graph could be one of the fault-tolerance measures for the graph G and the routing ρ and it is denoted by D(R(G, ρ)/F). We want to reduce the total number of routes defined in the routing, and the maximum of the number of routes defined for a node (called route degree) as least as possible. In this paper, we show that we can construct a routing λ for every n-node k-connected graph such that n ≥ 2k2, in which the route degree is O(k√n), the total number of routes is O(k2 n) and D(R(G, λ)/F) ≤ 3 for any fault set F(|F| k). We also show that we can construct a routing ρ1 for every n-node biconnected graphs, in which the total number of routes is O(n) and D(R(G, ρ1)/{f} ≤ 2 for any fault f, and using ρ1 a routing ρ2 for every n-node biconnected graphs, in which the route degree is O(√n), the total number of routes is O(n√n) and D(R(G; ρ2)/{f} ≤ 2 for any fault f.