Graph orientation problems with forbidden tournaments

Given a finite set of oriented graphs F, the F-free orientation problem is the following decision problem. Given a finite input graph, is there an orientation of its edges such that the resulting directed graph omits every member of F. If the set F consists of tournaments (i.e. complete oriented graphs), Bodirsky and Guzmán-Pro have recently established that this computational problem exhibits a complexity dichotomy: it is either solvable in polynomial time or NP-complete. I will explain how the F-free orientation problem can be viewed as the constraint satisfaction problem (CSP) of an omega-categorical template, making it amenable to universal algebraic methods. In particular I will demonstrate how the recently developed technique of "smooth approximations", provides a shorter algebraic proof of the complexity dichotomy for the graph orientation problem.

Publication Details

Journal
reposiTUm (TU Wien)
Published
2024-10-15
DOI
https://doi.org/10.34726/8500
Primary Topic
Plant Ecology and Soil Science
Type
article
Field-Weighted Citation Impact
0.00
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article

Graph orientation problems with forbidden tournaments

reposiTUm (TU Wien)
Plant Ecology and Soil Science
article

Graph orientation problems with forbidden tournaments

article en

Abstract

Given a finite set of oriented graphs F, the F-free orientation problem is the following decision problem. Given a finite input graph, is there an orientation of its edges such that the resulting directed graph omits every member of F. If the set F consists of tournaments (i.e. complete oriented graphs), Bodirsky and Guzmán-Pro have recently established that this computational problem exhibits a complexity dichotomy: it is either solvable in polynomial time or NP-complete. I will explain how the F-free orientation problem can be viewed as the constraint satisfaction problem (CSP) of an omega-categorical template, making it amenable to universal algebraic methods. In particular I will demonstrate how the recently developed technique of "smooth approximations", provides a shorter algebraic proof of the complexity dichotomy for the graph orientation problem.

reposiTUm (TU Wien)
Peace, Justice and strong institutions
Openalex Percentile: Top 48%
Plant Ecology and Soil Science
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