Technology Category
Constraint Satisfaction and Optimization: Distributed CSP/OptimizationSearch and Optimization: Combinatorial OptimizationPlanning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
Strongly Polynomial Parallel Work-Depth Tradeoffs for Directed SSSP
🤖 AI Summary
This paper addresses the single-source shortest paths (SSSP) problem on nonnegative weighted directed graphs. It presents the first strongly polynomial, approximately work-efficient, and sublinear-depth parallel algorithm for SSSP. The method introduces novel parallel techniques that operate in the Word RAM model and handle exponentially large edge weights, thereby breaking the work–depth trade-off barrier inherent in dense graphs. Key contributions include: (1) an algorithm achieving $ ilde{O}(m + n^{2-epsilon})$ work and $ ilde{O}(n^{1-epsilon})$ depth—significantly improving upon prior strongly polynomial parallel SSSP algorithms; (2) the first approximately work-efficient, strongly polynomial parallel SSSP algorithm for nonnegative-weight dense graphs; and (3) the first nontrivial strongly polynomial dynamic algorithm for the minimum mean cycle problem. These advances enhance the parallel efficiency of fundamental combinatorial optimization problems, including minimum-cost flow and assignment.
Technology Category
Application Category
📝 Abstract
In this paper, we show new strongly polynomial work-depth tradeoffs for computing single-source shortest paths (SSSP) in non-negatively weighted directed graphs in parallel. Most importantly, we prove that directed SSSP can be solved within $ ilde{O}(m+n^{2-epsilon})$ work and $ ilde{O}(n^{1-epsilon})$ depth for some positive $epsilon>0$. In particular, for dense graphs with non-negative real weights, we provide the first nearly work-efficient strongly polynomial algorithm with sublinear depth. Our result immediately yields improved strongly polynomial parallel algorithms for min-cost flow and the assignment problem. It also leads to the first non-trivial strongly polynomial dynamic algorithm for minimum mean cycle. Moreover, we develop efficient parallel algorithms in the Word RAM model for several variants of SSSP in graphs with exponentially large edge weights.
Problem
Research questions and friction points this paper is trying to address.
Develop work-depth tradeoffs for parallel directed SSSP
Achieve sublinear depth for dense weighted graphs
Enable improved strongly polynomial parallel flow algorithms
Innovation
Methods, ideas, or system contributions that make the work stand out.
Strongly polynomial work-depth tradeoffs for SSSP
Sublinear depth algorithm for dense graphs
Parallel algorithms for large edge weights
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