Making Locally Optimal Decisions on Graphs with Cycles

We present two new algorithms, LCM and IBFS, that make locally optimal incre-mental planning decisions for the task of nding a path to a goal state in a problem space that contains cycles. Earlier work (RTA* 10]) only solves this locally optimal decision problem when the problem space is tree structured. We precisely characterize the time and space complexity of both new algorithms, and show that they are asymptotically optimal. In addition, we present empirical evidence for a variety of maze problem spaces which shows that LCM and IBFS consistently produce shorter solutions than RTA*, and that the average computation cost of IBFS and LCM grows only slowly with the size of the problem. Finally, we show that as the lookahead depth increases, both algorithms require less computation per move decision than RTA*. An earlier version of this paper appeared in 15].