A robot has to explore an undirected connected graph by visiting all its nodes and traversing all edges. It may either have a complete a priori knowledge of the graph or only have an unoriented map of it, or, finally, lack any knowledge of the graph. We study the impact of this varying amount of knowledge on exploration performance. It is shown that the best exploration algorithm lacking any knowledge of the graph uses twice as many edge traversals in the worst case as does the best algorithm which has an unoriented map of the graph. On the other hand, the latter uses twice as many edge traversals in the worst case as does the best algorithm having a complete knowledge of the graph. Similar results for the restricted case of exploration algorithms working only for trees are also established. © 2000 John Wiley & Sons, Inc.

In this paper, we deal with 2-rearrangeable graphs, that is, graphs in which every permutation can be routed in two steps, such that each packet moves on a walk of length 2 without vertex-contention. We give necessary and sufficient conditions for a graph to be 2-rearrangeable. We end by proposing a construction of k-rearrangeable graphs, where k ≥ 2. © 1998 John Wiley & Sons, Inc. Networks 31: 239–247, 1998

We consider broadcasting a message from one node of a tree to all other nodes. In the presence of up to k link failures the tree becomes disconnected, and only nodes in the connected component C containing the source can be informed. The maximum ratio between the time used by a broadcasting scheme B to inform C and the optimal time to inform C, taken over all components C yielded by configurations of at most k faults, is the k-vulnerability of B. This is the maximum slowdown incurred by B due to the lack of a priori knowledge of fault location, for at most k faults. Since the upper bound k on the number of faults is not always known, it is important to design broadcasting schemes that behave well under any possible number of faults. It turns out that achieving the lowest possible k-vulnerability for all k simultaneously is impossible for some trees. Hence a natural goal is to seek, for any tree T, a broadcasting scheme that simultaneously approximates the lowest possible k-vulnerability for every k, up to a given constant factor c (independent of L). We describe a polynomial algorithm which decides if such a "universally fault-tolerant" broadcasting scheme exists for given T and c, and constructs such a scheme if it exists.