Interdisciplinary Information Sciences
Online ISSN : 1347-6157
Print ISSN : 1340-9050
ISSN-L : 1340-9050
Reviews and Lectures: Exploring the Limits of Computation
Arborescence Problems in Directed Graphs: Theorems and Algorithms
Naoyuki KAMIYAMA
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2014 Volume 20 Issue 1 Pages 51-70

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Abstract

In this survey, we consider arborescences in directed graphs. The concept of arborescences is a directed analogue of a spanning tree in an undirected graph, and one of the most fundamental concepts in graph theory and combinatorial optimization. This survey has two aims: we first show recent developments in the research on arborescences, and then give introduction of abstract concepts (e.g., matroids), and algorithmic techniques (e.g., primal-dual method) through well-known results for arborescences.
In the first half of this survey, we consider the minimum-cost arborescence problem. The goal of this problem is to find a minimum-cost arborescence rooted at a designated vertex, where a matroid and a primal-dual method play important roles. In the second half of this survey, we study the arborescence packing problem. The goal of this problem is to find arc-disjoint arborescences rooted at a designated vertex, where the min-max theorem by Edmonds plays an important role.

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© 2014 by the Graduate School of Information Sciences (GSIS), Tohoku University
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