Some practical planning problems can be interpreted as set-to-set shortest path problem (spp), i.e., as search of a shortest path between two sets of nodes, A and B, of a graph G. A straightforward reduction of such a problem to the search of solutions for point-to-point spps is impractical because the computational complexity is too high for a huge G. This paper presents a new approach to set-to-set spp for the case of not arbitrary A and B, but those which are represented by some nodes of an additional graph T . The graph T simulates a``geographic system'' on G. Under some assumptions natural for many applications, this approach leads to a competitive algorithm for this kind of set-to-set spp. As prospective areas for this technique, two applications are discussed± the problem of route planning for a visually guided robot in a static environment, and the problem of planning a fastest trip by means of all available timetables of all kinds of transport.

No abstract

No abstract

No abstract