We present new algorithms for k-coloring and minimum (/spl chi/(G)-) coloring random and semi-random k-colorable graphs in polynomial expected time. The random graphs are drawn from the G(n,p,k) model and the semi-random graphs are drawn from the G/sub SB/(n,p,k) model. In both models, an adversary initially splits the n vertices into k color classes, each of size /spl Theta/(n). Then the edges between vertices in different color classes are chosen one by one, according to some probability distribution. The model G/sub SB/(n,p,k) was introduced by A. Blum (1991) and with respect to randomness, it lies between the random model G(n,p,k) where all edges are chosen with equal probability and the worst-case model.
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机译:我们为K型k - 着色和最小(/ spl chi /(g) - )提出了新的算法,在多项式预期时间中着色随机和半随机k可色图。随机图是从G(n,p,k)模型中的绘制,并且从g / sub sb /(n,p,k)模型中汲取半随机图。在这两种模型中,对手最初将N个顶点分成K颜色类,每个尺寸/SPLθ/(n)。然后根据一些概率分布,逐个选中不同颜色类中的顶点之间的边缘。由A.Blum(1991)和随机性引入型号G / SUB SB /(N,P,K),它位于随机型号G(n,p,k)之间,其中所有边缘选择为等于概率和最坏情况模型。
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