On subbetweennesses of trees: Hardness, algorithms, and characterizations

Authors:
Dieter Rautenbach;Vinícius Fernandes dos Santos;Philipp M. Schäfer;Jayme L. Szwarcfiter
Affiliations:
Institut für Optimierung und Operations Research, Universität Ulm, D-89069 Ulm, Germany;Instituto de Matemática, NCE, and COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, Brazil;Institut für Optimierung und Operations Research, Universität Ulm, D-89069 Ulm, Germany;Instituto de Matemática, NCE, and COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, Brazil
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

We study so-called betweennesses induced by trees and forests. Algorithmic problems related to betweennesses are typically hard. They have been studied as relaxations of ordinal embeddings and occur for instance in psychometrics and molecular biology. Our contributions are hardness results, efficient algorithms, and structural insights such as complete axiomatic characterizations.