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3,214
Worst case complexity of direct search
, 2010
"... In this paper we prove that direct search of directional type shares the worst case complexity bound of steepest descent when sufficient decrease is imposed using a quadratic function of the step size parameter. This result is proved under smoothness of the objective function and using a framework o ..."
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Cited by 33 (4 self)
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In this paper we prove that direct search of directional type shares the worst case complexity bound of steepest descent when sufficient decrease is imposed using a quadratic function of the step size parameter. This result is proved under smoothness of the objective function and using a framework
On the WorstCase Complexity of the Silhouette of a Polytope
 IN 15TH CANADIAN CONFERENCE ON COMPUTATIONAL GEOMETRY  CCCG’03
, 2003
"... We give conditions under which the worstcase size of the silhouette of a polytope is sublinear. We provide examples with linear size silhouette if any of these conditions is relaxed. Our bounds are the first nontrivial bounds for the worstcase complexity of silhouettes. ..."
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Cited by 6 (3 self)
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We give conditions under which the worstcase size of the silhouette of a polytope is sublinear. We provide examples with linear size silhouette if any of these conditions is relaxed. Our bounds are the first nontrivial bounds for the worstcase complexity of silhouettes.
Cryptographic functions from worstcase complexity assumptions
, 2007
"... Lattice problems have been suggested as a potential source of computational hardness to beused in the construction of cryptographic functions that are provably hard to break. A remarkable feature of latticebased cryptographic functions is that they can be proved secure (that is,hard to break on t ..."
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Cited by 3 (1 self)
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on the average) based on the assumption that the underlying lattice problems are computationally hard in the worstcase. In this paper we give a survey of the constructions andproof techniques used in this area, explain the importance of basing cryptographic functions on the worstcase complexity of lattice
Worstcase complexity of the optimal LLL algorithm
 In Proceedings of LATIN’2000  Punta del Este. LNCS 1776
"... . In this paper, we consider the open problem of the complexity of the LLL algorithm in the case when the approximation parameter t of the algorithm has its extreme value 1. This case is of interest because the output is then the strongest Lovaszreduced basis. Experiments reported by Lagarias and ..."
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Cited by 8 (2 self)
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and Odlyzko [LO83] seem to show that the algorithm remain polynomial in average. However no bound better than a naive exponential order one is established for the worst case complexity of the optimal LLL algorithm, even for fixed small dimension (higher than 2). Here we prove that, for any fixed dimension n
The worst case complexity of Maximum Parsimony
"... Abstract. One of the core classical problems in computational biology is that of constructing the most parsimonious phylogenetic tree interpreting an input set of sequences from the genomes of evolutionarily related organisms. We reexamine the classical Maximum Parsimony (MP) optimization problem f ..."
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for the general (asymmetric) scoring matrix case, where rooted phylogenies are implied, and analyze the worst case bounds of three approaches to MP: The approach of CavalliSforza and Edwards (CavalliSforza and Edwards, 1967), the approach of Hendy and Penny (Hendy and Penny, 1982), and a new agglomerative
On the optimal order of worst case complexity of direct search
, 2015
"... Abstract The worst case complexity of directsearch methods has been recently analyzed when they use positive spanning sets and impose a sufficient decrease condition to accept new iterates. Assuming that the objective function is smooth, it is now known that such methods require at most O(n 2 −2 ) ..."
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Cited by 2 (1 self)
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Abstract The worst case complexity of directsearch methods has been recently analyzed when they use positive spanning sets and impose a sufficient decrease condition to accept new iterates. Assuming that the objective function is smooth, it is now known that such methods require at most O(n 2 −2
On the optimal order of worst case complexity of direct search
, 2015
"... The worst case complexity of directsearch methods has been recently analyzed when they use positive spanning sets and impose a sufficient decrease condition to accept new iterates. For smooth unconstrained optimization, it is now known that such methods require at most O(n2ϵ2) function evaluations ..."
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The worst case complexity of directsearch methods has been recently analyzed when they use positive spanning sets and impose a sufficient decrease condition to accept new iterates. For smooth unconstrained optimization, it is now known that such methods require at most O(n2ϵ2) function evaluations
Worst Case Complexity of Direct Search under Convexity
, 2014
"... In this paper we prove that the broad class of directsearch methods of directional type, based on imposing sufficient decrease to accept new iterates, exhibits the same worst case complexity bound and global rate of the gradient method for the unconstrained minimization of a convex and smooth funct ..."
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In this paper we prove that the broad class of directsearch methods of directional type, based on imposing sufficient decrease to accept new iterates, exhibits the same worst case complexity bound and global rate of the gradient method for the unconstrained minimization of a convex and smooth
WISE: Automated test generation for worstcase complexity
 in ICSE
, 2009
"... Program analysis and automated test generation have primarily been used to find correctness bugs. We present complexity testing, a novel automated test generation technique to find performance bugs. Our complexity testing algorithm, which we call WISE (Worstcase Inputs from Symbolic Execution), ope ..."
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Cited by 16 (1 self)
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Program analysis and automated test generation have primarily been used to find correctness bugs. We present complexity testing, a novel automated test generation technique to find performance bugs. Our complexity testing algorithm, which we call WISE (Worstcase Inputs from Symbolic Execution
On the Worstcase Complexity of Integer Gaussian Elimination
"... Abstract Gaussian elimination is the baais for classical algorithms for computing canonical forms of integer matrices. Experimental results have shown that integer Gaussian elimination may lead to rapid growth of intermediate entries. On the other hand various polynomial time algorithms do exist fo ..."
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that there is an exponential length lower bound onthe operands for swelldefined variant of Gaussian elimination when applied to Smith and Hermite normal form calculation, We present explicit matrices for which this variant produces exponential length entries. Thus, Gaussian elimination has worstcase exponential space
Results 1  10
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