On the Crossing Number of Almost Planar Graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F07%3A00021694" target="_blank" >RIV/00216224:14330/07:00021694 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
On the Crossing Number of Almost Planar Graphs
Original language description
Crossing minimization is one of the most challenging algorithmic problems in topological graph theory, with strong ties to graph drawing applications. Despite a long history of intensive research, no practical ``good'' algorithm for crossing minimizationis known (that is hardly surprising, since the problem itself is NP-complete). Even more surprising is how little we know about a seemingly simple particular pro-blem: to minimize the number of crossings in an {it almost planar} graph, that is, a graph with an edge whose removal leaves a planar graph. This problem is in turn a building block in an ``edge insertion'' heuristic for crossing minimization. In this paper we prove a constant factor approximation algorithm for the crossing number of almostplanar graphs with bounded degree. On the other hand, we demonstrate nontriviality of the crossing minimization problem on almost planar graphs by exhibiting several examples, among them new families of crossing critical graphs which are
Czech name
O průsečíkovém čísle téměř planárních grafů
Czech description
Dokážeme Delta-aproximační algoritmus pro výpočet průsečíkového čísla téměř planárních grafů.

Project
<a href="/en/project/1M0545" target="_blank" >1M0545: Institute for Theoretical Computer Science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2007
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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