Abstract
The surviving route graph R( G, ϱ) for a graph G, a routing ϱ and 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 (denoted by D( R( G, ϱ))) could be one of the fault-tolerance measures for the graph G and the routing ϱ. In this paper, we show that we can construct a routing ϱ for any biconnected graph G such that D( R( G, ϱ)/{ f}) ⩽ 2 for any fault f, and a routing λ for any connected graph G' such that D( R( G', λ)/{ f'}⩽2 if G' -{ f'} is connected for any fault f'. We also show that both routings can be computed in linear time.
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