A New Single-Source Shortest Path Algorithm for Nonnegative Weight Graph

TL;DR

This paper introduces a new single-source shortest path algorithm for nonnegative weight graphs that reduces Fibonacci heap operations, achieving comparable or better performance than Dijkstra's algorithm in certain cases.

Contribution

The paper proposes a novel shortest path algorithm that compresses multiple heap operations into one, improving efficiency over traditional Fibonacci heap-based methods.

Findings

Algorithm has worst-case complexity of O(m + n log n).

It can achieve linear time in specific scenarios.

Demonstrates faster average performance than Dijkstra's algorithm with Fibonacci heap.

Abstract

The single-source shortest path problem is a classical problem in the research field of graph algorithm. In this paper, a new single-source shortest path algorithm for nonnegative weight graph is proposed. The algorithm can compress multi-round Fibonacci heap operations to one round to save running time relative to Dijkstra's algorithm using Fibonacci heap. The time complexity of the algorithm is also O(m+nlogn) in the worst case, where m is the number of edges and n is the number of nodes. However, the bound can be linear in some case, for example, when edge weights of a graph are all the same and the hop count of the longest shortest path is much less than n.Based on the theoretical analyses, we demonstrate that the algorithm is faster than Dijkstra's algorithm using Fibonacci heap in average situation when n is large enough.