Negative-Weight Single-Source Shortest Paths in Near-Linear Time

Abstract

In the single-source shortest paths problem, the goal is to compute the shortest path tree from a designated source vertex in a weighted, directed graph. We present the first near-linear time algorithm for the problem that can also handle negative edge-weights; the runtime is O(mlog8(n)logW).In contrast to all recent developments that rely on sophisticated continuous optimization methods and dynamic algorithms, our algorithm is simple: it requires only a simple graph decomposition and elementary combinatorial tools. In fact, ours is the first combinatorial algorithm for negative-weight single-source shortest paths to break through the classic O∼(mnlogW) bound from over three decades ago (Gabow and Tarjan, SICOMP'89.).