The efficiency of randomized parallel backtrack search

We present a refined analysis of the randomized parallel backtrack search algorithm (RPBS) of Karp and Zhang (1993). It is shown that the total number of messages occurred in the execution of RPBS is likely to be O(hp log d) where h and d are the height and degree of the backtrack search tree and p is the number of processors used. As a consequence, under the assumption of unit-time message delivery, the execution time of RPBS is likely to be n/p+O(h log d). Given its limited amount of communication, RPBS can be efficiently implemented in a message-passing or shared-memory multiprocessor systems. A general analysis of network implementation of RPBS is given. Some experimental data are also presented