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A copositive programming approach to graph partitioning
Povh, Janez, 1973- ; Rendl, Franz
V članku obravnavamo problem delitve točk grafa na tri množice ▫$S_1$▫, ▫$S_2$▫ in ▫$S_3$▫ s predpisano močjo, tako da je skupna teža vseh povezav med ▫$S_1$▫ in ▫$S_2$▫ minimalna. Problem je tesno ...povezan z nekaterimi NP-težkimi problemi kot so npr. iskanje pasovne širine grafa in iskanje ločilca točk grafa. V članku pokažemo, da lahko ta problem zapišemo kot linearen program nad stožcem popolnoma pozitivnih matrik, kar nakaže naravno pot do semidefinitnih poenostavitev problema. Pokažemo tudi, da lahko spektralno poenostavitev, ki so jo predstavili Helmberg et al. (1995), zapišemo ekvivalentno kot semidefinitni program. Predlagamo tudi strožjo različico tega semidefinitnega programa in pokažemo na manjših grafih, da s tem dobimo bistveno boljšo spodnjo mejo od tiste, ki temelji na spektralni poenostavitvi.
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