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arXiv · 1509.02841

Approximating the Smallest Spanning Subgraph for 2-Edge-Connectivity in Directed Graphs

Loukas Georgiadis·Giuseppe F. Italiano·Charis Papadopoulos·Nikos Parotsidis
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Abstract

Let $G$ be a strongly connected directed graph. We consider the following three problems, where we wish to compute the smallest strongly connected spanning subgraph of $G$ that maintains respectively: the $2$-edge-connected blocks of $G$ (\textsf{2EC-B}); the $2$-edge-connected components of $G$ (\textsf{2EC-C}); both the $2$-edge-connected blocks and the $2$-edge-connected components of $G$ (\textsf{2EC-B-C}). All three problems are NP-hard, and thus we are interested in efficient approximation algorithms. For \textsf{2EC-C} we can obtain a $3/2$-approximation by combining previously known results. For \textsf{2EC-B} and \textsf{2EC-B-C}, we present new $4$-approximation algorithms that run in linear time. We also propose various heuristics to improve the size of the computed subgraphs in practice, and conduct a thorough experimental study to assess their merits in practical scenarios.

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Loukas Georgiadis, Giuseppe F. Italiano, Charis Papadopoulos, Nikos Parotsidis. 2015-09-09. Approximating the Smallest Spanning Subgraph for 2-Edge-Connectivity in Directed Graphs. https://arxiv.org/abs/1509.02841

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