منابع مشابه
A new upper bound for Achlioptas processes
We consider here on-line algorithms for Achlioptas processes. Given a initially empty graph G on n vertices, a random process that at each step selects independently and uniformly at random two edges from the set of non-edges is launched. We must choose one of the two edges and add it to the graph while discarding the other. The goal is to avoid the appearance of a connected component spanning ...
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We show that a randomly chosen 3-CNF formula over n variables with clauses-tovariables ratio at least 4.4898 is asymptotically almost surely unsatisfiable. The previous best such bound, due to Dubois in 1999, was 4.506. The first such bound, independently discovered by many groups of researchers since 1983, was 5.19. Several decreasing values between 5.19 and 4.506 were published in the years b...
متن کاملCancellative pairs of families of sets
A pair (~, ~) of families of subsets of an n-element set X is cancellative if, for all A, A' e .~ and B, B' E ~, the following conditions hold: A\B = A ' \ B ~ A =A' and BkA =B'kA~B = B'. We prove that every such pair satisfies I.~11~1 < 0 ~, where 0 ~2.3264. This is related to a conjecture of ErdSs and Katona on cancellative families and to a conjecture of Simonyi on recovering pairs. For the ...
متن کاملA new bound for map labeling with uniform circle pairs
Given a planar point set, we wish to label the points with uniform circular labels such that each input point lies on the boundary of two labels, none of the interiors of the labels intersect, and the size of the labels is maximized. This problem is known as map-labeling with uniform circular pairs (MLUCP) and has been shown to be NP-hard. In this paper, we give an O(n logn) time, O(n) space al...
متن کاملNew Worst-Case Upper Bound for #XSAT
An algorithm running in O(1.1995) is presented for counting models for exact satisfiability formulae(#XSAT). This is faster than the previously best algorithm which runs in O(1.2190). In order to improve the efficiency of the algorithm, a new principle, i.e. the common literals principle, is addressed to simplify formulae. This allows us to eliminate more common literals. In addition, we firstl...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2018
ISSN: 1077-8926
DOI: 10.37236/7210