A reduction of the logspace shortest path problem to biconnected graphs

TL;DR

This paper introduces a novel approach to solving the shortest path problem in logspace by reducing it to biconnected graphs, including a new linear time algorithm for specific graph classes.

Contribution

It presents a reduction of the logspace shortest path problem to biconnected graphs and a new linear time, logspace algorithm for graphs with bounded degree and component size.

Findings

Logspace shortest path algorithm for general graphs using a biconnected graph oracle.

Linear time, logspace shortest path algorithm for graphs with bounded degree and component size.

Optimal asymptotic time-space product among shortest path algorithms.

Abstract

In this paper, we reduce the logspace shortest path problem to biconnected graphs; in particular, we present a logspace shortest path algorithm for general graphs which uses a logspace shortest path oracle for biconnected graphs. We also present a linear time logspace shortest path algorithm for graphs with bounded vertex degree and biconnected component size, which does not rely on an oracle. The asymptotic time-space product of this algorithm is the best possible among all shortest path algorithms.