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3,854,237
and Fixed Point Computation
"... In this paper, we give a lower bound of Ω(n (d−1)/2) on the quantum query complexity for finding a fixed point of a discrete Brouwer function over grid [1: n] d. Our bound is nearly tight, as the Grover search algorithm can be used to find a fixed point with O(n d/2) quantum queries. Our result esta ..."
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establishes a nearly tight bound for the computation of ddimensional approximate Brouwer fixed points as defined by Scarf and by Hirsch, Papadimitriou, and Vavasis. It can also be extended to the quantum model for Sperner’s Lemma in any dimensions: The quantum query complexity of finding a panchromatic cell
Iterative Algorithms for Fixed Point Computation
, 1993
"... W e comparetwo algorithmsforcomputingflxedpointsoffunctionalsofthekindarisinginstaticprogramanalysis. One isa rather directcalculationoftheiterands,whereastheotheremploysthetechniqueofiterative squaring.To give meaningfulresultsaboutthetime and spacerequirementswe needtobe morespeciflc abouttheform ..."
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W e comparetwo algorithmsforcomputingflxedpointsoffunctionalsofthekindarisinginstaticprogramanalysis. One isa rather directcalculationoftheiterands,whereastheotheremploysthetechniqueofiterative squaring.To give meaningfulresultsaboutthetime and spacerequirementswe needtobe morespeciflc abouttheform ofthefunctionalsandthepropertiesofthefunctionsupon which the functionalsoperate.Inthispaperwe considerfunctionalsiniterative versus(two kindsof)primitiverecursiveforms,andfunctionsthatare monotoneversuscompletelyadditive. The timecomplexity ofthedirectalgorithmisproportionalto thenumberofiterationsand thesizeofthedomainofthefunctions. Replacingthedirectalgorithmwiththeiterative squaringalgorithm givesan exponentialreductioninthenum berofiterationsneeded.If theprogramanalysiscanbe formulatedinthecompletelyadditive framework,wewillinsomeinstances obtainanexponentialreduction inthecostofeach iteration. 1 Introduction Thepurposeofstaticprogramanalysisistogetinformationaboutprograms withoutact...
Quantum separation of local search and fixed point computation
 Proceedings of the 14th Annual International Computing and Combinatorics Conference, 2008
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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Cited by 2 (2 self)
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
Derivation Tree Analysis for Accelerated FixedPoint Computation
"... Abstract. We show that for several classes of idempotent semirings the least fixedpoint of a polynomial system of equations X = f(X) is equal to the least fixedpoint of a linear system obtained by “linearizing ” the polynomials of f in a certain way. Our proofs rely on derivation tree analysis, a ..."
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Cited by 3 (3 self)
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proof principle that combines methods from algebra, calculus, and formal language theory, and was first used in [5] to show that Newton’s method over commutative and idempotent semirings converges in a linear number of steps. Our results lead to efficient generic algorithms for computing the least fixedpoint
An Analog Scheme for FixedPoint Computation–Part II: Applications
"... Abstract—In a companion paper [6] we presented theoretical analysis of an analog network for fixedpoint computation. This paper applies these results to several applications from numerical analysis and combinatorial optimization, in particular: 1) solving systems of linear equations; 2) nonlinear p ..."
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Abstract—In a companion paper [6] we presented theoretical analysis of an analog network for fixedpoint computation. This paper applies these results to several applications from numerical analysis and combinatorial optimization, in particular: 1) solving systems of linear equations; 2) nonlinear
INVESTIGATION OF FIXEDPOINT COMPUTATION INFLUENCE ON NUMERICAL SOLUTIONS OF FRACTIONAL DIFFERENTIAL EQUATIONS
"... Abstract: In this paper the problem of the influence of fixed point computation on numerical solutions of linear differential equations of fractional order is considered. It is a practically important problem, because of potential possibilities of using dynamical systems of fractional order in the t ..."
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Abstract: In this paper the problem of the influence of fixed point computation on numerical solutions of linear differential equations of fractional order is considered. It is a practically important problem, because of potential possibilities of using dynamical systems of fractional order
A Syntactic Approach to Fixed Point Computation on Finite Domains
 In Proc. 1992 ACM Symposium on Lisp and Functional Programming
, 1992
"... We propose a syntactic approach to performing fixed point computation on finite domains. Finding fixed points in finite domains for monotonic functions is an essential task when calculating abstract semantics of functional programs. Previous methods for fixed point finding have been mainly based on ..."
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We propose a syntactic approach to performing fixed point computation on finite domains. Finding fixed points in finite domains for monotonic functions is an essential task when calculating abstract semantics of functional programs. Previous methods for fixed point finding have been mainly based
Iterative fixed point computation for typebased strictness analysis
 In Proceedings from SAS '94, number 864 in Lecture Notes in Computer Science
, 1994
"... Amtoft has formulated an “online ” constraint normalization method for solving a strictness inference problem inspired by Wright. From the syntactic form of the normalized constraints he establishes that every program expression has a unique, most precise (“minimal”) strictness judgement, given fix ..."
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Cited by 3 (0 self)
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iterative fixed point methods in a second phase. The main result follows from the fact that observable negative strictness variables only occur on the righthand sides of the constraints. Furthermore, a standard iterative fixed point algorithm solves the constraints in linear time in the number
An Optimal Algorithm for Approximate Nearest Neighbor Searching in Fixed Dimensions
 ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 1994
"... Consider a set S of n data points in real ddimensional space, R d , where distances are measured using any Minkowski metric. In nearest neighbor searching we preprocess S into a data structure, so that given any query point q 2 R d , the closest point of S to q can be reported quickly. Given any po ..."
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Cited by 983 (32 self)
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query point q 2 R d , and ffl ? 0, a (1 + ffl)approximate nearest neighbor of q can be computed in O(c d;ffl log n) time, where c d;ffl d d1 + 6d=ffle d is a factor depending only on dimension and ffl. In general, we show that given an integer k 1, (1 + ffl)approximations to the k nearest neighbors
Results 1  10
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3,854,237