Network-based vertex dissolution

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

doi:10.1137/140978880

Network-based vertex dissolution

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

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

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.

Original language	English
Pages (from-to)	888-914
Number of pages	27
Journal	SIAM Journal on Discrete Mathematics
Volume	29
Issue number	2
DOIs	https://doi.org/10.1137/140978880
State	Published - 1 Jan 2015
Externally published	Yes

Keywords

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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10.1137/140978880

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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.",

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AU - Bredereck, Robert

AU - Chen, Jiehua

AU - Froese, Vincent

AU - Niedermeier, Rolf

AU - Woeginger, Gerhard J.

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KW - Computational complexity analysis

KW - Economization

KW - Election control

KW - Flow networks

KW - Matching

KW - NP-hard problems

KW - Political districting

KW - Redistribution scenarios

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Network-based vertex dissolution

Abstract

Keywords

ASJC Scopus subject areas

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