Searching for authors named "Dimitris Achlioptas" – sorted by Relevance.
48 documents found, showing 1 through 10.
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Random Matrices in Data Analysis
- …We show how carefully crafted random matrices can achieve distance-preserving dimensionality reduction, accelerate spectral computations, and reduce the sample complexity of certain kernel methods.…
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Setting 2 variables at a time yields a new lower bound for random 3-SAT (Extended Abstract)
- …Let X be a set of n Boolean variables and denote by C(X) the set of all 3-clauses over X, i.e. the set of all 8 n 3 possible disjunctions of three distinct, non-complementary literals from variables in X. Let F (n; m) be a random 3-SAT formula formed by selecting, with replacement, m clauses uniform…
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Lower bounds for random 3-SAT via differential equations
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Threshold Phenomena in Random Graph Colouring and Satisfiability
- … We study threshold phenomena pertaining to the colourability of random graphs and the satisfiability of random formulas. Consider a random graph G(n, p) on n vertices formed by including each of the possible edges independently of all others with probability p. For a fixed integer k, let f k …
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Database-friendly Random Projections
- …A classic result of Johnson and Lindenstrauss asserts that any set of n points in d-dimensional Euclidean space can be embedded into k-dimensional Euclidean space | where k is logarithmic in n and independent of d | so that all pairwise distances are maintained within an arbitrarily small factor. Al…
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The Threshold for Random k-SAT is 2^k (ln 2 + o(1))
- …Let Fk (n, m) be a random k-SAT formula with n variables and m clauses selected uniformly and independently among all 2 possible k-clauses. It is well-known that if r ln 2 then Fk (n, rn) is unsatisfiable with probability 1 o(1). We prove that there exists a sequence t k = O(k) such that if t k , th…
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Random k-SAT: two moments suffice to cross a sharp threshold
- …Abstract. Many NP-complete constraint satisfaction problems appear to undergo a “phase transition” from solubility to insolubility when the constraint density passes through a critical threshold. In all such cases it is easy to derive upper bounds on the location of the threshold by showing that abo…
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On the 2-Colorability of Random Hypergraphs
- …A 2-coloring of a hypergraph is a mapping from its vertices to a set of two colors such that no edge is monochromatic. Let Hk (n; m) be a random k-uniform hypergraph on n vertices formed by picking m edges uniformly, independently and with replacement. It is easy to show that if r rc = 2 ln …
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The Analysis of a List-Coloring Algorithm on a Random Graph (Extended Abstract)
- …We introduce a natural k-coloring algorithm and analyze its performance on random graphs with constant expected degree c (G n;p=c=n ). For k = 3 our results imply that almost all graphs with n vertices and 1:923 n edges are 3-colorable. This improves the lower bound on the threshold for random 3-col…
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Almost All Graphs With 2.522n Edges Are Not 3-Colorable
- …We prove that for c 2:522 a random graph with n vertices and m = cn edges is not 3-colorable with probability 1 o(1). Similar bounds for non-k-colorability are given for k > 3.…
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