Time-Space Tradeoffs for Undirected Graph Traversal by Graph Automata

We investigate time-space tradeoffs for traversing undirected graphs, using a variety of structured models that are all variants of Cook and Rackoff's ``Jumping Automata for Graphs.'' Our strongest tradeoff is a quadratic lower bound on the product of time and space for graph traversal. For example, achieving linear time requires linear space, implying that depth-first search is optimal. Since our bound in fact applies to nondeterministic algorithms for nonconnectivity, it also implies that closure under complementation of nondeterministic space-bounded complexity classes is achieved only at the expense of increased time. To demonstrate that these structured models are realistic, we also investigate their power. In addition to admitting well known algorithms such as depth-first search and random walk, we show that one simple variant of this model is nearly as powerful as a Turing machine. Specifically, for general undirected graph problems, it can simulate a Turing machine with only a constant factor increase in space and a polynomial factor increase in time. ] 1996 Academic Press article no. 0085