Directed Graph Minors and Serial-Parallel Width

Authors Argyrios Deligkas, Reshef Meir



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Argyrios Deligkas
  • Leverhulme Research Centre, University of Liverpool, UK
Reshef Meir
  • Faculty of Industrial Engineering and Management, Technion, Israel

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Argyrios Deligkas and Reshef Meir. Directed Graph Minors and Serial-Parallel Width. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 44:1-44:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.MFCS.2018.44

Abstract

Graph minors are a primary tool in understanding the structure of undirected graphs, with many conceptual and algorithmic implications. We propose new variants of directed graph minors and directed graph embeddings, by modifying familiar definitions. For the class of 2-terminal directed acyclic graphs (TDAGs) our two definitions coincide, and the class is closed under both operations. The usefulness of our directed minor operations is demonstrated by characterizing all TDAGs with serial-parallel width at most k; a class of networks known to guarantee bounded negative externality in nonatomic routing games. Our characterization implies that a TDAG has serial-parallel width of 1 if and only if it is a directed series-parallel graph. We also study the computational complexity of finding a directed minor and computing the serial-parallel width.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Mathematics of computing → Graph theory
Keywords
  • directed minors
  • pathwidth

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