Space-Efficient Parallel Algorithms for Combinatorial Search Problems

We present space-efficient parallel strategies for two fundamental combinatorial search problems, namely, \emph{backtrack search} and \emph{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 distributed-memory machine with $p$ processors. For backtrack search, we give a deterministic algorithm running in $\BO{n/p+h\log p}$ time, and a Las Vegas algorithm requiring optimal $\BO{n/p+h}$ time, with high probability. Building on the backtrack search algorithm, we also derive a Las Vegas algorithm for branch-and-bound which runs in $\BO{(n/p+h\log p \log n)h\log n}$ 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 previously known algorithms whose space requirements per processor depend on the (possibly huge) tree to be explored ($\BOM{h}$ for backtrack search and $\BOM{n/p}$ for branch-and-bound).