Finding k-Dissimilar Paths with Minimum Collective Length

TL;DR

This paper addresses the problem of finding multiple dissimilar paths in road networks with minimal total length, introducing an exact algorithm and scalable heuristics that balance solution quality and computational efficiency.

Contribution

It presents an exact algorithm for k-Dissimilar Paths with Minimum Collective Length and scalable heuristics based on simple single-via paths.

Findings

Exact algorithm reduces computational cost with pruning techniques.

Iterating over simple single-via paths offers scalable solutions.

Trade-off between solution quality and scalability demonstrated.

Abstract

Shortest path computation is a fundamental problem in road networks. However, in many real-world scenarios, determining solely the shortest path is not enough. In this paper, we study the problem of finding k-Dissimilar Paths with Minimum Collective Length (kDPwML), which aims at computing a set of paths from a source s to a target t such that all paths are pairwise dissimilar by at least \theta and the sum of the path lengths is minimal. We introduce an exact algorithm for the kDPwML problem, which iterates over all possible s-t paths while employing two pruning techniques to reduce the prohibitively expensive computational cost. To achieve scalability, we also define the much smaller set of the simple single-via paths, and we adapt two algorithms for kDPwML queries to iterate over this set. Our experimental analysis on real road networks shows that iterating over all paths is impractical, while iterating over the set of simple single-via paths can lead to scalable solutions with only a small trade-off in the quality of the results.