On Crossing Sets, Disjoint Sets and the Pagenumber 1
نویسندگان
چکیده
Let G = (V;E) be a t-partite graph with n vertices and m edges, where the partite sets are given. We present an O(n2m1:5) time algorithm to construct drawings of G in the plane so that the size of the largest set of pairwise crossing edges, and at the same time, the size of the largest set of disjoint (pairwise non-crossing) edges are O(pt m). As an application we embed G in a book of O(pt m) pages, in O(n2m1:5) time, resolving an open question for the pagenumber problem. A similar result is obtained for the dual of the pagenumber or the queuenumber. Our algorithms are obtained by derandomizing a probabilistic proof.
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