A tighter insertion-based approximation of the crossing number

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F17%3A00094634" target="_blank" >RIV/00216224:14330/17:00094634 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1007/s10878-016-0030-z" target="_blank" >http://dx.doi.org/10.1007/s10878-016-0030-z</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10878-016-0030-z" target="_blank" >10.1007/s10878-016-0030-z</a>

Result language

angličtina

Original language name

A tighter insertion-based approximation of the crossing number

Original language description

Let G be a planar graph and F a set of additional edges not yet in G. The multiple edge insertion problem (MEI) asks for a drawing of G+F with the minimum number of pairwise edge crossings, such that the subdrawing of G is plane. Finding an exact solution to MEI is NP-hard for general F. We present the first polynomial time algorithm for MEI that achieves an additive approximation guarantee—depending only on the size of F and the maximum degree of G, in the case of connected G. Our algorithm seems to be the first directly implementable one in that realm, too, next to the single edge insertion. It is also known that an (even approximate) solution to the MEI problem would approximate the crossing number of the F-almost-planar graph G+F, while computing the crossing number of G+F exactly is NP-hard already when |F|=1. Hence our algorithm induces new, improved approximation bounds for the crossing number problem of F-almost-planar graphs, achieving constant-factor approximation for the large class of such graphs of bounded degrees and bounded size of F.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

<a href="/en/project/GA14-03501S" target="_blank" >GA14-03501S: Parameterized algorithms and kernelization in the context of discrete mathematics and logic</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2017

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Combinatorial Optimization

ISSN

1382-6905

e-ISSN

—

Volume of the periodical

33

Issue of the periodical within the volume

4

Country of publishing house

DE - GERMANY

Number of pages

43

Pages from-to

1183-1225

UT code for WoS article

000398945100003

EID of the result in the Scopus database

2-s2.0-85028255701