English

Network-Based Vertex Dissolution

Discrete Mathematics 2016-01-12 v3 Data Structures and Algorithms Social and Information Networks Combinatorics

Abstract

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.

Keywords

Cite

@article{arxiv.1402.2664,
  title  = {Network-Based Vertex Dissolution},
  author = {René van Bevern and Robert Bredereck and Jiehua Chen and Vincent Froese and Rolf Niedermeier and Gerhard J. Woeginger},
  journal= {arXiv preprint arXiv:1402.2664},
  year   = {2016}
}

Comments

Version accepted at SIAM Journal on Discrete Mathematics

R2 v1 2026-06-22T03:06:10.587Z