K-Shortest Simple Paths Using Biobjective Path Search

TL;DR

This paper presents a novel algorithm for the k-Shortest Simple Paths problem that transforms it into biobjective shortest path instances, achieving competitive asymptotic complexity and practical efficiency.

Contribution

It introduces a new approach converting the scalar k-Shortest Simple Paths problem into biobjective instances, filling a gap in existing algorithms.

Findings

Efficient in practice on grid graphs and road networks.

Matches state-of-the-art asymptotic running time.

Demonstrates practical effectiveness of the biobjective approach.

Abstract

In this paper we introduce a new algorithm for the \emph{$k$-Shortest Simple Paths} (\kspp{k}) problem with an asymptotic running time matching the state of the art from the literature. It is based on a black-box algorithm due to \citet{Roditty12} that solves at most $2k$ instances of the \emph{Second Shortest Simple Path} (\kspp{2}) problem without specifying how this is done. We fill this gap using a novel approach: we turn the scalar \kspp{2} into instances of the Biobjective Shortest Path problem. Our experiments on grid graphs and on road networks show that the new algorithm is very efficient in practice.