Finding Colorful Paths in Temporal Graphs

TL;DR

This paper investigates the problem of finding color-diverse paths in vertex-colored temporal graphs, analyzing its computational difficulty, proposing a heuristic solution, and evaluating its performance on various datasets.

Contribution

It introduces a new variant of the path-finding problem in temporal graphs, analyzes its approximation complexity, and provides a heuristic with experimental validation.

Findings

The problem is hard to approximate due to inapproximability bounds.

The proposed heuristic performs well on synthetic and real-world graphs.

Experimental results demonstrate the heuristic's effectiveness in maximizing color diversity.

Abstract

The problem of finding paths in temporal graphs has been recently considered due to its many applications. In this paper we consider a variant of the problem that, given a vertex-colored temporal graph, asks for a path whose vertices have distinct colors and include the maximum number of colors. We study the approximation complexity of the problem and we provide an inapproximability lower bound. Then we present a heuristic for the problem and an experimental evaluation of our heuristic, both on synthetic and real-world graphs.