Digraph measures: Kelly decompositions, games, and orderings

  • Authors:

  • Paul Hunter;Stephan Kreutzer

  • Affiliations:

  • Humboldt-University Berlin and Isaac Newton Institute, Cambridge;Humboldt-University Berlin and Isaac Newton Institute, Cambridge

  • Venue:
  • SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
  • Year:
  • 2007

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Abstract

We consider various well-known, equivalent complexity measures for graphs such as elimination orderings, κ-trees and cops and robber games and study their natural translations to digraphs. We show that on digraphs all these measures are also equivalent and induce a natural connectivity measure. We introduce a decomposition for digraphs and an associated width, Kelly-width, which is equivalent to the aforementioned measure. We demonstrate its usefulness by exhibiting a number of potential applications including polynomial-time algorithms for NP-complete problems on graphs of bounded Kelly-width, and complexity analysis of asymmetric matrix factorization. Finally, we compare the new width to other known decompositions of digraphs.