A practical Single Source Shortest Path algorithm for random directed graphs with arbitrary weight in expecting linear time

TL;DR

This paper introduces the Raffica algorithm, a practical SSSP method that achieves expected linear time on random directed graphs with arbitrary weights, including detection of negative cycles.

Contribution

The paper presents a novel linear-time SSSP algorithm applicable to random graphs with arbitrary weights, extending beyond traditional assumptions.

Findings

Expected linear time complexity on random graphs.

Effective detection of negative cycles.

Applicable to various graph structures like grid graphs.

Abstract

In this paper, I present an algorithm called Raffica algorithm for Single-Source Shortest Path(SSSP). On random graph, this algorithm has linear time complexity(in expect). More precisely, the random graph uses configuration model, and the weights are distributed mostly positively. It is also linear for random grid graphs. Despite I made an assumption on the weights of the random graph, this algorithm is able to solve SSSP with arbitrary weights; when a negative cycle exists, this algorithm can find it out once traversed. The algorithm has a lot of appliances.