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An improved upper bound for SAT
 IN PROCEEDINGS OF THE 8TH INTERNATIONAL CONFERENCE ON THEORY AND APPLICATIONS ON SATISFIABILITY TESTING, SAT 2005
, 2005
"... We give a randomized algorithm for testing satisfiability of Boolean formulas in conjunctive normal form with no restriction on clause length. Its running time is at most 2 n(1−1/α) up to a polynomial factor, where α = ln(m/n) + O(ln ln m) and n, m are respectively the number of variables and the ..."
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Cited by 10 (1 self)
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and the number of clauses in the input formula. This bound is asymptotically better than the previously best known 2 n(1−1 / log(2m)) bound for SAT.
Improved upper bounds for 3sat
 In 15th ACMSIAM Symposium on Discrete Algorithms (SODA 2004). ACM and SIAM
"... The CNF Satisfiability problem is to determine, given a CNF formula F, whether or not there exists a satisfying assignment for F. If each clause of F contains at most k literals, then F is called a kCNF formula and the problem is called kSAT. For small k’s, especially for k = 3, there exists a lot ..."
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Cited by 48 (3 self)
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lot of algorithms which run significantly faster than the trivial 2n bound. The following list summarizes those algorithms where a constant c means that the algorithm runs in time O(cn). Roughly speaking most algorithms are based on DavisPutnam. [Sch99] is the first local search algorithm which gives
Improved Upper Bounds on Stopping Redundancy
, 2007
"... For a linear block code with minimum distance d, its stopping redundancy is the minimum number of check nodes in a Tanner graph representation of the code, such that all nonempty stopping sets have size d or larger. We derive new upper bounds on stopping redundancy for all linear codes in general, ..."
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Cited by 29 (4 self)
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, and for maximum distance separable (MDS) codes specifically, and show how they improve upon previous results. For MDS codes, the new bounds are found by upperbounding the stopping redundancy by a combinatorial quantity closely related to Turán numbers. (The Turán number, „
Improved Upper Bounds on Sizes of Codes
 IEEE TRANS. INFORM. THEORY
, 2002
"... Let A(n, d) denote the maximum possible number of codewords in a binary code of length and minimum Hamming distance . For large values of , the best known upper bound, for fixed , is the Johnson bound. We give a new upper bound which is at least as good as the Johnson bound for all values of and , a ..."
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Cited by 7 (2 self)
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Let A(n, d) denote the maximum possible number of codewords in a binary code of length and minimum Hamming distance . For large values of , the best known upper bound, for fixed , is the Johnson bound. We give a new upper bound which is at least as good as the Johnson bound for all values
Improved upper bounds on the crossing number
 SCG'08
, 2008
"... The crossing number of a graph is the minimum number of crossings in a drawing of the graph in the plane. Our main result is that every graph G that does not contain a fixed graph as a minor has crossing number O(∆n), where G has n vertices and maximum degree ∆. This dependence on n and ∆ is best po ..."
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Cited by 4 (0 self)
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possible. This result answers an open question of Wood and Telle [New York J. Mathematics, 2007], who proved the best previous bound of O(∆2n). In addition, we prove that every K5minorfree graph G has crossing number at most 2 P v deg(v) 2, which again is the best possible dependence on the degrees of G
Implications of Improved Upper Bounds on ∆L  = 2 Processes
, 2000
"... We discuss implications of improved upper bounds on the ∆L  = 2 processes (i) K + → π − µ + µ +, from an experiment at BNL, and (ii) µ − → e + conversion, from an experiment at PSI. In particular, we address the issue of constraints on neutrino masses and mixing, and on supersymmetric models wit ..."
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Cited by 1 (0 self)
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We discuss implications of improved upper bounds on the ∆L  = 2 processes (i) K + → π − µ + µ +, from an experiment at BNL, and (ii) µ − → e + conversion, from an experiment at PSI. In particular, we address the issue of constraints on neutrino masses and mixing, and on supersymmetric models
Improved Upper Bound for the Redundancy of FixFree Codes
 IEEE Tran. Inform. Theory
, 2003
"... A variablelength code is a fixfree code if no codeword is a prefix or a suffix of any other codeword. In fixfree code any finite sequence of codewords can be decoded in both directions, which can improve robustness to channel noise and speed up the decoding process. In this paper we prove a new s ..."
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Cited by 6 (0 self)
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sufficient condition for existence of fixfree codes and improve upper bound on the redundancy of optimal fixfree codes.
Simplicity is beauty: improved upper bounds for Vertex Cover
, 2005
"... Abstract — This paper presents an O(1.2738 k + kn)time polynomialspace algorithm for VERTEX COVER improving both the previous O(1.286 k +kn)time polynomialspace algorithm by Chen, Kanj, and Jia, and the very recent O(1.2745 k k 4 + kn)time exponentialspace algorithm, by Chandran and Grandoni. M ..."
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Cited by 20 (0 self)
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as generalizations of previous techniques, are introduced including: general folding, struction, tuples, and local amortized analysis. The algorithm also induces improvement on the upper bound for the INDEPENDENT SET problem on graphs of degree bounded by 6. I.
Results 1  10
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1,327,733