We present space-efficient parallel strategies for two fundamental
combinatorial search problems, namely, backtrack search and branch-and-bound,
both involving the visit of an n-node tree of height h under the assumption
that a node can be accessed only through its father or its children. For both
problems we propose efficient algorithms that run on a p-processor
distributed-memory machine. For backtrack search, we give a deterministic
algorithm running in O(n/p+hlogp) time, and a Las Vegas algorithm requiring
optimal O(n/p+h) time, with high probability. Building on the backtrack
search algorithm, we also derive a Las Vegas algorithm for branch-and-bound
which runs in O((n/p+hlogplogn)hlog2n) time, with high probability. A
remarkable feature of our algorithms is the use of only constant space per
processor, which constitutes a significant improvement upon previous algorithms
whose space requirements per processor depend on the (possibly huge) tree to be
explored.Comment: Extended version of the paper in the Proc. of 38th International
Symposium on Mathematical Foundations of Computer Science (MFCS