Space-Efficient Parallel Algorithms for Combinatorial Search Problems

Andrea Pietracaprina, Geppino Pucci, Francesco Silvestri, Fabio Vandin

Abstract: 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 distributed-memory machine with p processors. For backtrack search, we give a deterministic algorithm running in ${O}\left(n/p+h\log p\right)$ time, and a Las Vegas algorithm requiring optimal ${O}\left(n/p+h\right)$ time, with high probability. Building on the backtrack search algorithm, we also derive a Las Vegas algorithm for branch-and-bound which runs in ${O}\left((n/p+h\log p \log n)h\log n\right)$ 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 ( ${\Omega}\left(h\right)$ for backtrack search and ${\Omega}\left(n/p\right)$ for branch-and-bound).