Polylogarithmic-overhead piecemeal graph exploration

Abstract

We introduce a new traversal technique in the context of piecemeal exploration of unknown graphs. The problem of learning a graph via piecemeal exploration requires a robot to create a complete map of its environment, subject to two constraints. First, it cannot jump between non-adjacent vertices in one time step and second, it must return to a fixed starting point every so often. This paper presents the recursive piecemeal search (RPS) strategy together with an algorithm for the above problem. We are able to achieve O(log 2 n) overhead (where n is the number of vertices), improving on previous results of Awerbuch, Betke, Rivest, and Singh which require O(n ffl ) overhead. The graph is discovered via the recursive piecemeal search, which can be viewed as a combination of breadth-first and depth-first passes. The construction of RPS trees relies on the concept of sparse neighborhood covers and captures nicely the nature of the graph exploration problem. This paper is eligible for ...