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Algorithms for the edge-width of an embedded graphCabello, Sergio ; Colin de Verdière, Éric, 1977- ; Lazarus, FrancisNaj bo ▫$G$▫ neutežen graf kompleksnosti ▫$n$▫, ki je vložen v ploskev roda ▫$g$▫. Prikazan je izboljšani algoritem za določanje dolžine najkrajšega nestisljivega in najkrajšega neseparirajočega ... cikla v grafu. Za vsako naravno število ▫$k$▫ lahko najdemo tak cikel v času ▫$O(gnk)$▫, če je njegova dolžina kvečjemu ▫$k$▫. V nasprotnem primeru pa ugotovimo, da je dolžina večja od ▫$k$▫. Tako za poljubno izbrano ploskev lahko preverimo v linearnem času, če je povezavna ali celična širina vloženega grafa večja od ▫$k$▫. Prikazan je tudi aproksimacijski algoritem za iskanje najkrajšega netrivialnega cikla. Pri poljubnem danem parametru ▫$\varepsilon$▫ (▫$0< \varepsilon < 1$▫) dobimo v času ▫$O(gn/\varepsilon)$▫ netrivialni cikel, katerega dolžina je kvečjemu za faktor ▫$1+\varepsilon$▫ večja od najkrajšega takega cikla.Source: 26th Annual Symposium on Computation Geometry at Snowbird, Utah, USA : Special issue (Str. 215-224)Type of material - conference contributionPublish date - 2012Language - englishCOBISS.SI-ID - 16093017
source: 26th Annual Symposium on Computation Geometry at Snowbird, Utah, USA : Special issue (Str. 215-224)
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Cabello, Sergio | 25993 |
Colin de Verdière, Éric, 1977- | |
Lazarus, Francis |
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