Simple Greedy Algorithms for Fundamental Multidimensional Graph Problems

Bilò, Vittorio; Caragiannis, Ioannis; Fanelli, Angelo; Flammini, Michele; Monaco, Gianpiero

doi:10.4230/LIPIcs.ICALP.2017.125

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Simple Greedy Algorithms for Fundamental Multidimensional Graph Problems

Authors Vittorio Bilò, Ioannis Caragiannis, Angelo Fanelli, Michele Flammini, Gianpiero Monaco

Part of: Volume: 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: International Colloquium on Automata, Languages, and Programming (ICALP)
License: Creative Commons Attribution 3.0 Unported license
Publication Date: 2017-07-07

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Document Identifiers

DOI: 10.4230/LIPIcs.ICALP.2017.125
URN: urn:nbn:de:0030-drops-74669

Subject Classification

Keywords

multidimensional graph problems
matroids
shortest paths
Steiner trees
arborescences

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Abstract

We revisit fundamental problems in undirected and directed graphs, such as the problems of computing spanning trees, shortest paths, steiner trees, and spanning arborescences of minimum cost. We assume that there are d different cost functions associated with the edges of the input graph and seek for solutions to the resulting multidimensional graph problems so that the p-norm of the different costs of the solution is minimized. We present combinatorial algorithms that achieve very good approximations for this objective. The main advantage of our algorithms is their simplicity: they are as simple as classical combinatorial graph algorithms of Dijkstra and Kruskal, or the greedy algorithm for matroids.

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Vittorio Bilò, Ioannis Caragiannis, Angelo Fanelli, Michele Flammini, and Gianpiero Monaco. Simple Greedy Algorithms for Fundamental Multidimensional Graph Problems. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 125:1-125:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.ICALP.2017.125

Author Details

Vittorio Bilò

Ioannis Caragiannis

Angelo Fanelli

Michele Flammini

Gianpiero Monaco

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