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Construction of roadmaps in semi-algebraic sets
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1007/3-540-51084-2_28openalex-snapshot
Generalized characteristic polynomials
inferredcites →https://doi.org/10.1007/3-540-54522-0_99openalex-snapshot
Computing roadmaps of general semi-algebraic sets
inferredcites →https://doi.org/10.1007/978-1-4612-0441-1_14openalex-snapshot
On the Complexity of Zero-dimensional Algebraic Systems
inferredcites →https://doi.org/10.1007/978-1-4612-0441-1_5openalex-snapshot
On algorithms for real algebraic plane curves
inferredcites →https://doi.org/10.1007/978-1-4612-2628-4_28openalex-snapshot
Single Exponential Path Finding in Semi-algebraic Sets, Part II: The General Case
inferredcites →https://doi.org/10.1007/bf01202001openalex-snapshot
Counting connected components of a semialgebraic set in subexponential time
inferredcites →https://doi.org/10.1007/bf01614146openalex-snapshot
Finding connected components of a semialgebraic set in subexponential time
inferredcites →https://doi.org/10.1016/0304-3975(83)90002-6openalex-snapshot
Definability and fast quantifier elimination in algebraically closed fields
inferredcites →https://doi.org/10.1016/s0747-7171(08)80012-0openalex-snapshot
Generalised characteristic polynomials
inferredcites →https://doi.org/10.1016/s0747-7171(88)80005-1openalex-snapshot
Solving systems of polynomial inequalities in subexponential time
inferredcites →https://doi.org/10.1016/s0747-7171(88)80006-3openalex-snapshot
Complexity of deciding Tarski algebra
inferredcites →https://doi.org/10.1090/s0002-9939-1964-0161339-9openalex-snapshot
On the Betti Numbers of Real Varieties
inferredcites →https://doi.org/10.1109/sfcs.1987.1openalex-snapshot
A new algebraic method for robot motion planning and real geometry
inferredcites →https://doi.org/10.24033/bsmf.2138openalex-snapshot
Sur la complexité du principe de Tarski-Seidenberg
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
inferred← citeshttps://doi.org/10.1007/3-540-33099-2_17openalex-snapshot
Computing Roadmaps and Connected Components of Semi-algebraic Sets
inferred← citeshttps://doi.org/10.1007/978-3-642-13411-1_5openalex-snapshot
An Efficient Algorithm for the Sign Condition Problem in the Semi-algebraic Context
inferred← citeshttps://doi.org/10.1007/978-3-662-05355-3_12openalex-snapshot
Polynomial System Solving
inferred← citeshttps://doi.org/10.1007/978-3-662-05355-3_17openalex-snapshot
Computing Roadmaps and Connected Components of Semi-algebraic Sets
inferred← citeshttps://doi.org/10.1007/bf02573999openalex-snapshot
Description of the connected components of a semialgebraic set in single exponential time
inferred← citeshttps://doi.org/10.1007/pl00009443openalex-snapshot
On Bounding the Betti Numbers and Computing the Euler Characteristic of Semi-Algebraic Sets
inferred← citeshttps://doi.org/10.1007/s00037-005-0190-1openalex-snapshot
Computing the euler–poincaré characteristics of sign conditions
inferred← citeshttps://doi.org/10.1007/s00454-009-9239-2openalex-snapshot
A Baby Steps/Giant Steps Probabilistic Algorithm for Computing Roadmaps in Smooth Bounded Real Hypersurface
inferred← citeshttps://doi.org/10.1007/s00454-014-9610-9openalex-snapshot
Divide and Conquer Roadmap for Algebraic Sets
inferred← citeshttps://doi.org/10.1007/s00454-024-00626-0openalex-snapshot
Efficient Computation of a Semi-Algebraic Basis of the First Homology Group of a Semi-Algebraic Set
inferred← citeshttps://doi.org/10.1007/s10208-005-0208-8openalex-snapshot
Computing the Top Betti Numbers of Semialgebraic Sets Defined by Quadratic Inequalities in Polynomial Time
inferred← citeshttps://doi.org/10.1007/s10208-007-9001-1openalex-snapshot
Computing the First Betti Number of a Semi-Algebraic Set
inferred← citeshttps://doi.org/10.1007/s10208-008-9033-1openalex-snapshot
Errata for Computing the Top Betti Numbers of Semialgebraic Sets Defined by Quadratic Inequalities in Polynomial Time
inferred← citeshttps://doi.org/10.1007/s10208-010-9062-4openalex-snapshot
Polynomial Hierarchy, Betti Numbers, and a Real Analogue of Toda’s Theorem
inferred← citeshttps://doi.org/10.1007/s10208-014-9212-1openalex-snapshot
A Baby Step–Giant Step Roadmap Algorithm for General Algebraic Sets
inferred← citeshttps://doi.org/10.1007/s10958-006-0111-0openalex-snapshot
Computing the dimension of a semi-algebraic set
inferred← citeshttps://doi.org/10.1016/b978-044482537-7/50003-6openalex-snapshot
Arrangements and Their Applications**Work by PA. was supported by Army Research Office MURI grant DAAH04-96-1-0013, by a Sloan fellowship, by an NYI award, and by a grant from the U.S.–Israeli Binational Science Foundation. Work by M.S. was supported by NSF Grants CCR-91-22103 and CCR-93-11127, by…
inferred← citeshttps://doi.org/10.1016/j.cagd.2020.101858openalex-snapshot
Numerical roadmap of smooth bounded real algebraic surface
inferred← citeshttps://doi.org/10.1016/j.jalgebra.2008.09.043openalex-snapshot
Computing the Betti numbers of semi-algebraic sets defined by partly quadratic systems of polynomials
inferred← citeshttps://doi.org/10.1016/j.jsc.2006.07.001openalex-snapshot
Computing the first few Betti numbers of semi-algebraic sets in single exponential time
inferred← citeshttps://doi.org/10.1016/j.jsc.2025.102532openalex-snapshot
Computing roadmaps in unbounded smooth real algebraic sets II: Algorithm and complexity
inferred← citeshttps://doi.org/10.1016/s0747-7171(03)00085-3openalex-snapshot
Algorithms to compute the topology of orientable real algebraic surfaces
inferred← citeshttps://doi.org/10.1017/9781009701259.006openalex-snapshot
Betti Number Bounds, Applications and Algorithms
inferred← citeshttps://doi.org/10.1090/conm/453/08799openalex-snapshot
Algorithmic semi-algebraic geometry and topology—recent progress and open problems
inferred← citeshttps://doi.org/10.1090/conm/697/14046openalex-snapshot
Efficient algorithms for computing the Euler-Poincaré characteristic of symmetric semi-algebraic sets
inferred← citeshttps://doi.org/10.1090/s0894-0347-99-00311-2openalex-snapshot
Computing roadmaps of semi-algebraic sets on a variety
inferred← citeshttps://doi.org/10.1109/focs.2009.70openalex-snapshot
Polynomial Hierarchy, Betti Numbers and a Real Analogue of Toda's Theorem
inferred← citeshttps://doi.org/10.1109/synasc.2010.91openalex-snapshot
Connectivity in Semi-algebraic Sets
inferred← citeshttps://doi.org/10.1145/1060590.1060636openalex-snapshot
Computing the first Betti number and the connected components of semi-algebraic sets
inferred← citeshttps://doi.org/10.1145/2442829.2442831openalex-snapshot
Complexity of deciding connectivity in real algebraic sets
inferred← citeshttps://doi.org/10.1145/281508.281533openalex-snapshot
Complexity of computing semi-algebraic descriptions of the connected components of a semi-algebraic set
inferred← citeshttps://doi.org/10.1145/2996450openalex-snapshot
A Nearly Optimal Algorithm for Deciding Connectivity Queries in Smooth and Bounded Real Algebraic Sets
inferred← citeshttps://doi.org/10.1145/3208976.3209023openalex-snapshot
Real Root Finding for Equivariant Semi-algebraic Systems
inferred← citeshttps://doi.org/10.1145/3666000.3669687openalex-snapshot
Connectivity in Symmetric Semi-Algebraic Sets
inferred← citeshttps://doi.org/10.1145/780506.780518openalex-snapshot
Computing the topology of real algebraic surfaces
inferred← citeshttps://doi.org/10.48550/arxiv.0902.1612openalex-snapshot
A baby steps/giant steps Monte Carlo algorithm for computing roadmaps in smooth compact real hypersurfaces
inferred← citeshttps://doi.org/10.48550/arxiv.1201.6439openalex-snapshot
A baby step-giant step roadmap algorithm for general algebraic sets
inferred← citeshttps://doi.org/10.48550/arxiv.1409.1534openalex-snapshot
Algorithms in Real Algebraic Geometry: A Survey
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