Space-Efficient Parallel Algorithms for Combinatorial Search Problems

TL;DR

This paper introduces space-efficient parallel algorithms for backtrack search and branch-and-bound problems, achieving optimal or near-optimal time complexity with constant space per processor on distributed-memory systems.

Contribution

It presents novel space-efficient parallel algorithms for combinatorial search problems that operate with constant space per processor, improving upon previous methods.

Findings

Deterministic backtrack search runs in O(n/p+h log p) time.

Las Vegas backtrack search achieves O(n/p+h) time with high probability.

Branch-and-bound algorithm runs in near-optimal time with high probability.

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 $p$-processor distributed-memory machine. For backtrack search, we give a deterministic algorithm running in $O(n/p+h\log p)$ 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 $O((n/p+h\log p \log n)h\log^2 n)$ 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 previous algorithms whose space requirements per processor depend on the (possibly huge) tree to be explored.