Fast Priority Queues for Parallel Branch-and-Bound

Currently used parallel best rst branch-and-bound algorithms either suuer from contention at a centralized priority queue or can only approximate the best rst strategy. Bottleneck free algorithms for parallel priority queues are known but they cannot be implemented very eeciently on contemporary machines. We present quite simple randomized algorithms for parallel priority queues on distributed memory machines. For branch-and-bound they are asymptotically as eecient as previously known PRAM algorithms with high probability. The simplest versions require not much more communication than the approximated branch-and-bound algorithm of Karp and Zhang.