An efficient algorithm to add up-links to a rooted tree to obtain a minimum cost 2-connected graph-Reference-Cited by-同舟云学术

An efficient algorithm to add up-links to a rooted tree to obtain a minimum cost 2-connected graph

Published:2024-07-21 Issue: Volume: Page:63-67
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Container-title:Anais do IX Encontro de Teoria da Computação (ETC 2024)
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Author:

Azevedo Gabriel Morete de,Wakabayashi Yoshiko

Abstract

We present an efficient algorithm to solve a special case of the following node-connectivity augmentation problem. Given a tree T = (V,E) and an additional set L ⊂ (V 2) of edges, called links, L ∩ E = ∅, each one with a rational nonnegative cost, find a minimum cost set of links F ⊆ L such that T + F is 2-connected. In general form, this problem is NP-hard. We focus on the up-link variation, where the tree T has a root, and every link is an edge from a node to its ancestor. We present a linear formulation for this problem together with a proof of integrality and an efficient combinatorial algorithm for it.

Publisher

Sociedade Brasileira de Computação - SBC

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