A tighter insertion-based approximation of the crossing number

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

A tighter insertion-based approximation of the crossing number

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

A tighter insertion-based approximation of the crossing number

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

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

Projekt

<a href="/cs/project/GA14-03501S" target="_blank" >GA14-03501S: Parametrizované algoritmy a kernelizace v kontextu diskrétní matematiky a logiky</a><br>

Návaznosti

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

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Journal of Combinatorial Optimization

ISSN

1382-6905

e-ISSN

—

Svazek periodika

33

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

43

Strana od-do

1183-1225

Kód UT WoS článku

000398945100003

EID výsledku v databázi Scopus

2-s2.0-85028255701