Parallel Label-Setting Multi-objective Shortest Path Search

Abstract

We present a parallel algorithm for finding all Pareto optimal paths from a specified source in a graph. The algorithm is label-setting, i.e., it only performs work on distance labels that are optimal. The main result is that the added complexity when going from one to multiple objectives is completely parallelizable. The algorithm is based on a multiobjective generalization of a priority queue. Such a Pareto queue can be efficiently implemented for two dimensions. Surprisingly, the parallel biobjective approach yields an algorithm performing asymptotically less work than the previous sequential algorithms. We also discuss generalizations for d ≥ 3 objective functions and for single target search.

Parallel Bi-objective Shortest Paths Using Weight-Balanced B-trees with Bulk Updates

“…The final balanced result is computed by concatenating the resulting trees which is possible in logarithmic time. In [19] this result is generalized to accommodate the operations needed for paPaSearch. In principle, this approach can be extended to B-trees resulting in better cache-efficiency than [6,8,11] Here we go one step further by using weight-balanced B-trees [3].…”

“…This way we get easily predictable highly coarse grained re-balancing by partial rebuilding and we naturally integrate dynamic load balancing by work stealing. This makes our solution more elegant and robust than [19] since [6,19] uses both static explicit load balancing for bulk updates and dynamic load balancing for finding Pareto optima.…”

“…Covering both the theoretical results of [19] and our own contribution in sufficient detail is beyond the scope of this work. For that reason, we only focus on our implementation, giving as numerous details as possible for the many parts in which we divert from the original result; see the Appendix for further details.…”

“…This is indeed a problem for the single-objective case. However, Sanders and Mandow show that in multi-objective search, at least for the bi-objective case [19], all additional work is parallelizable. Unfortunately, while conceptually simple, their paPaSearch-algorithm looks complicated and forbiddingly expensive.…”

“…This is much more cache efficient than comparable solutions based on binary trees. Based on this, Section 3.2 introduces a streamlined implementation of paPaSearch that reduces the number of processing phases compared to [19] and uses more coarse grained parallelism. The experimental evaluation in Section 4 demonstrates that an implementation using the Intel Threading Building Blocks achieves speedups up to 8 using 16 cores.…”