Network-based vertex dissolution

René Van Bevern, Robert Bredereck, Jiehua Chen, Vincent Froese, Rolf Niedermeier, Gerhard J. Woeginger

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


We introduce a graph-theoretic vertex dissolution model that applies to a number of redistribution scenarios, such as gerrymandering in political districting or work balancing in an online situation. The central aspect of our model is the deletion of certain vertices and the redistribution of their load to neighboring vertices in a completely balanced way. We investigate how the underlying graph structure, the knowledge of which vertices should be deleted, and the relation between old and new vertex loads influence the computational complexity of the underlying graph problems. Our results establish a clear borderline between tractable and intractable cases.

Original languageEnglish
Pages (from-to)888-914
Number of pages27
JournalSIAM Journal on Discrete Mathematics
Issue number2
StatePublished - 1 Jan 2015
Externally publishedYes


  • Combinatorial algorithms
  • Computational complexity analysis
  • Economization
  • Election control
  • Flow networks
  • Matching
  • NP-hard problems
  • Political districting
  • Redistribution scenarios

ASJC Scopus subject areas

  • General Mathematics


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