L. E. Kavraki, J.-C. Latombe, R. Motwani, and P. Raghavan, “Randomized Query Processing in Robot Path Planning,” Journal of Computer and System Sciences, vol. 57, no. 1, pp. 50–60, Aug. 1998.
The subject of this paper is the analysis of a randomized preprocessing scheme that has been used for query processing in robot path planning. The attractiveness of the scheme stems from its general applicability to virtually any path-planning problem, and its empirically observed success. In this paper we initiate a theoretical basis for explaining this empirical success. Under a simple assumption about the configuration space, we show that it is possible to perform preprocessing following which queries can be answered quickly. En route, we consider related problems on graph connectivity in the evasiveness model and art-gallery theorems.