A parallel algorithm for the single step searching problem

Introduces the single-step searching problem, which is defined as follows. We are given a graph where each vertex is associated with a weight. Assume that every edge of graph is of equal length. A fugitive may be hidden in any edge. We are asked to assign searchers to vertices to search the entire graph in one step such that no fugitive can escape. The cost of a searching plan is related to the weights of the vertices in which the searchers are initially located. Our goal is to minimize the cost of the searching plan. A parallel algorithm based upon The EREW model is proposed to solve this problem. This algorithm applies the tree contraction technique. The critical point is that we have to transform a general tree into a binary tree, including pseudo-nodes, in order to apply this tree contraction technique. A new algorithm is devised to solve the problem on the transformed binary tree. It can be proved that this new algorithm is correct, as it produces a correct solution for the original tree. Our algorithm has an optimal speed-up.<>