Computing a Minimum Color Path in Edge-Colored Graphs

  • Neeraj KumarEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11544)


In this paper, we study the problem of computing a min-color path in an edge-colored graph. More precisely, we are given a graph \(G=(V, E)\), source s, target t, an assignment \(\chi :E \rightarrow 2^{\mathcal {C}}\) of edges to a set of colors in \(\mathcal {C}\), and we want to find a path from s to t such that the number of unique colors on this path is minimum over all possible \(s-t\) paths. We show that this problem is hard (conditionally) to approximate within a factor \(O(n^{1/8})\) of optimum, and give a polynomial time \(O(n^{2/3})\)-approximation algorithm. We translate the ideas used in this approximation algorithm into two simple greedy heuristics, and analyze their performance on an extensive set of synthetic and real world datasets. From our experiments, we found that our heuristics perform significantly better than the best previous heuristic algorithm for the problem on all datasets, both in terms of path quality and the running time.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of CaliforniaSanta BarbaraUSA

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