NP-Completeness of Max-Cut for Segment Intersection Graphs

Oswin Aichholzer; Wolfgang Mulzer; Partick Schnider; Birgit Vogtenhuber

NP-Completeness of Max-Cut for Segment Intersection Graphs

Oswin Aichholzer, Wolfgang Mulzer, Partick Schnider, Birgit Vogtenhuber

Institute of Software Technology (7160)

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

Abstract

We consider the problem of finding a maximum cut in a graph $G = (V, E)$, that is, a partition $ V_1 dotcup V_2$ of $V$ such that the number of edges between $V_1$ and $V_2$ is maximum. It is well known that the decision problem whether $G$ has a cut of at least a given size is in general NP-complete. We show that this problem remains hard when restricting the input to segment intersection graphs. These are graphs whose vertices can be drawn as straight-line segments, where two vertices share an edge if and only if the corresponding segments intersect. We obtain our result by a reduction from a variant of Planar Max-2-SAT that we introduce and also show to be NP-complete.

Original language	English
Title of host publication	Proc. $34^th$ European Workshop on Computational Geometry EuroCG '18
Place of Publication	Berlin, Germany
Pages	32:1-32:6
Publication status	Published - 2018

Cite this

@inproceedings{5432617cd1cf4f8291d61f41104df65e,

title = "NP-Completeness of Max-Cut for Segment Intersection Graphs",

abstract = "We consider the problem of finding a maximum cut in a graph $G = (V, E)$, that is, a partition $ V_1 dotcup V_2$ of $V$ such that the number of edges between $V_1$ and $V_2$ is maximum. It is well known that the decision problem whether $G$ has a cut of at least a given size is in general NP-complete. We show that this problem remains hard when restricting the input to segment intersection graphs. These are graphs whose vertices can be drawn as straight-line segments, where two vertices share an edge if and only if the corresponding segments intersect. We obtain our result by a reduction from a variant of Planar Max-2-SAT that we introduce and also show to be NP-complete.",

author = "Oswin Aichholzer and Wolfgang Mulzer and Partick Schnider and Birgit Vogtenhuber",

year = "2018",

language = "English",

pages = "32:1--32:6",

booktitle = "Proc. $34^th$ European Workshop on Computational Geometry EuroCG '18",

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TY - GEN

T1 - NP-Completeness of Max-Cut for Segment Intersection Graphs

AU - Aichholzer, Oswin

AU - Mulzer, Wolfgang

AU - Schnider, Partick

AU - Vogtenhuber, Birgit

PY - 2018

Y1 - 2018

N2 - We consider the problem of finding a maximum cut in a graph $G = (V, E)$, that is, a partition $ V_1 dotcup V_2$ of $V$ such that the number of edges between $V_1$ and $V_2$ is maximum. It is well known that the decision problem whether $G$ has a cut of at least a given size is in general NP-complete. We show that this problem remains hard when restricting the input to segment intersection graphs. These are graphs whose vertices can be drawn as straight-line segments, where two vertices share an edge if and only if the corresponding segments intersect. We obtain our result by a reduction from a variant of Planar Max-2-SAT that we introduce and also show to be NP-complete.

AB - We consider the problem of finding a maximum cut in a graph $G = (V, E)$, that is, a partition $ V_1 dotcup V_2$ of $V$ such that the number of edges between $V_1$ and $V_2$ is maximum. It is well known that the decision problem whether $G$ has a cut of at least a given size is in general NP-complete. We show that this problem remains hard when restricting the input to segment intersection graphs. These are graphs whose vertices can be drawn as straight-line segments, where two vertices share an edge if and only if the corresponding segments intersect. We obtain our result by a reduction from a variant of Planar Max-2-SAT that we introduce and also show to be NP-complete.

M3 - Conference paper

SP - 32:1-32:6

BT - Proc. $34^th$ European Workshop on Computational Geometry EuroCG '18

CY - Berlin, Germany

ER -