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One model of message delivery in a computer network is based on labellingeach edge by a subset of a (reasonably small) universal set, and then encodinga path as the union of the labels of its edges. Earlier work suggested usingrandom edge labels, and that approach has a disadvantage of producing errors(false positives). We demonstrate that if we make an assumption about the shapeof the network (in this paper we consider networks with a dense core and atree-like periphery) and assume that messages are delivered along shortestpaths, we can label edges in a way which prevents any false positives.

Encoding shortest paths in graphs assuming the code is queried using bit-wise comparison