Sur la complexité du principe de Tarski-Seidenberg

Heintz, Joos; Roy, Marie-Françoise; Solernó, Pablo

doi:10.24033/bsmf.2138

Cited by 105 publications

(55 citation statements)

References 11 publications

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“…Collins (1975) gave the first reasonable worst-case time bound for this problem. Grigor'ev and Vorobjov (1988) gave the first algorithm that was sub-doubly-exponential in the number of variables, and a number of following results improved the complexity in various ways (Canny, 1993;Heintz et al, 1990;Renegar, 1992). We use a result of Basu et al (2003), which has an improved asymptotic running time.…”

Section: Analysis Of Running Timementioning

confidence: 99%

A Polynomial-Time Algorithm for De Novo Protein Backbone Structure Determination from Nuclear Magnetic Resonance Data

Wang

Mettu

Donald

2006

Journal of Computational Biology

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We describe an efficient algorithm for protein backbone structure determination from solution Nuclear Magnetic Resonance (NMR) data. A key feature of our algorithm is that it finds the conformation and orientation of secondary structure elements as well as the global fold in polynomial time. This is the first polynomial-time algorithm for de novo high-resolution biomacromolecular structure determination using experimentally recorded data from either NMR spectroscopy or X-ray crystallography. Previous algorithmic formulations of this problem focused on using local distance restraints from NMR (e.g., nuclear Overhauser effect [NOE] restraints) to determine protein structure. This approach has been shown to be NP-hard, essentially due to the local nature of the constraints. In practice, approaches such as molecular dynamics and simulated annealing, which lack both combinatorial precision and guarantees on running time and solution quality, are used routinely for structure determination. We show that residual dipolar coupling (RDC) data, which gives global restraints on the orientation of internuclear bond vectors, can be used in conjunction with very sparse NOE data to obtain a polynomial-time algorithm for structure determination. Furthermore, an implementation of our algorithm has been applied to six different real biological NMR data sets recorded for three proteins. Our algorithm is combinatorially precise, polynomialtime, and uses much less NMR data to produce results that are as good or better than previous approaches in terms of accuracy of the computed structure as well as running time.

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Section: Analysis Of Running Timementioning

confidence: 99%

A Polynomial-Time Algorithm for De Novo Protein Backbone Structure Determination from Nuclear Magnetic Resonance Data

Wang

Mettu

Donald

2006

Journal of Computational Biology

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“…Although we were not able to derive a better worst case upper bound as (n n d) O(n) for the invariant δ i (see Propositions 6.1 and 6.3 below) the worst case complexity of the procedure Π i meets the already known extrinsic bound of (n d) O(n) for the elimination problem under consideration (compare the original papers [20,11,30,25,26,27,31,8] and the comprehensive book [9]). The complexity of the procedure Π i depends polynomially on the extrinsic parameters L, , n and d and on the degree δ i of the real interpretation of the equation system F 1 = 0, .…”

Section: Statement Of the Resultsmentioning

confidence: 98%

Polar, bipolar and copolar varieties: Real solving of algebraic varieties with intrinsic complexity

Bank¹,

Giusti²,

Heintz³

2013

Recent Advances in Real Complexity and Computation

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This survey covers a decade and a half of joint work with L. Lehmann, G. M. Mbakop, and L. M. Pardo. We address the problem of finding a smooth algebraic sample point for each connected component of a real algebraic variety, being only interested in components which are generically smooth locally complete intersections. The complexity of our algorithms is essentially polynomial in the degree of suitably defined generalized polar varieties and is therefore intrinsic to the problem under consideration.

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“…Although we were not able to derive a better worst case bound as (n n d) O(n) for the invariant δ i (see Proposition 8,12 and Observation 11 below) the worst case complexity of the procedure Π i meets the already known extrinsic bound of (n d) O(n) for the elimination problem under consideration (compare the original papers [24,12,34,28,29,29,30,35,9] and the comprehensive book [10]). …”

Section: Introductionmentioning

confidence: 99%

Point searching in real singularcomplete intersection varieties: algorithms of intrinsic complexity

2013

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Sur la complexité du principe de Tarski-Seidenberg

Cited by 105 publications

References 11 publications

A Polynomial-Time Algorithm for De Novo Protein Backbone Structure Determination from Nuclear Magnetic Resonance Data

A Polynomial-Time Algorithm for De Novo Protein Backbone Structure Determination from Nuclear Magnetic Resonance Data

Polar, bipolar and copolar varieties: Real solving of algebraic varieties with intrinsic complexity

Point searching in real singularcomplete intersection varieties: algorithms of intrinsic complexity

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