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Description of the connected components of a semialgebraic set in single exponential time

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1007/3-540-07407-4_17openalex-snapshot
Quantifier elimination for real closed fields by cylindrical algebraic decompostion
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IX. Ein Entscheidungsverfahren für die Theorie der reell-abgeschlossenen Körper
inferredcites →https://doi.org/10.1007/3-540-54195-0_50openalex-snapshot
Single exponential path finding in semialgebraic sets Part I: The case of a regular bounded hypersurface
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/bf01200148openalex-snapshot
Construction of roadmaps in semi-algebraic sets
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/10.1007/bfb0016236openalex-snapshot
Parallel arithmetic computations: A survey
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On the “piano movers” problem. II. General techniques for computing topological properties of real algebraic manifolds
inferredcites →https://doi.org/10.1016/s0747-7171(10)80003-3openalex-snapshot
On the computational complexity and geometry of the first-order theory of the reals. Part I: Introduction. Preliminaries. The geometry of semi-algebraic sets. The decision problem for the existential theory of the reals
inferredcites →https://doi.org/10.1016/s0747-7171(10)80004-5openalex-snapshot
On the computational complexity and geometry of the first-order theory of the reals. Part II: The general decision problem. Preliminaries for quantifier elimination
inferredcites →https://doi.org/10.1016/s0747-7171(10)80005-7openalex-snapshot
On the computational complexity and geometry of the first-order theory of the reals. Part III: Quantifier elimination
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/10.1142/9789812791245openalex-snapshot
Data Structures and Algorithms
inferredcites →https://doi.org/10.1145/62212.62257openalex-snapshot
Some algebraic and geometric computations in PSPACE
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.

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Computing Roadmaps and Connected Components of Semi-algebraic Sets
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Expressing topological connectivity of spatial databases
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Real Algebraic Geometry and Constraint Databases
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Single Exponential Path Finding in Semi-algebraic Sets, Part II: The General Case
inferred← citeshttps://doi.org/10.1007/978-3-540-45072-6_20openalex-snapshot
Region-Based Query Languages for Spatial Databases in the Topological Data Model
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_17openalex-snapshot
Computing Roadmaps and Connected Components of Semi-algebraic Sets
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
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Computing the Top Betti Numbers of Semialgebraic Sets Defined by Quadratic Inequalities in Polynomial Time
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Computing the First Betti Number of a Semi-Algebraic Set
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Errata for Computing the Top Betti Numbers of Semialgebraic Sets Defined by Quadratic Inequalities in Polynomial Time
inferred← citeshttps://doi.org/10.1007/s10440-012-9782-3openalex-snapshot
Numerically Computing Real Points on 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…
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Computing the Betti numbers of semi-algebraic sets defined by partly quadratic systems of polynomials
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Counting complexity classes for numeric computations II: Algebraic and semialgebraic sets
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.2022.09.003openalex-snapshot
Smooth points on semi-algebraic sets
inferred← citeshttps://doi.org/10.1016/s0022-0000(02)00034-xopenalex-snapshot
Reachability and connectivity queries in constraint databases
inferred← citeshttps://doi.org/10.1090/conm/453/08799openalex-snapshot
Algorithmic semi-algebraic geometry and topology—recent progress and open problems
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Towards a theory of movie database queries
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Exact Algorithms for Linear Matrix Inequalities
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Counting complexity classes for numeric computations II
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Computing the first Betti number and the connected components of semi-algebraic sets
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On bounding the Betti numbers and computing the Euler characteristic of semi-algebraic sets
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Verified error bounds for real solutions of positive-dimensional polynomial systems
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Polytime algorithm for the shortest path in a homotopy class amidst semi-algebraic obstacles in the plane
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Complexity of computing semi-algebraic descriptions of the connected components of a semi-algebraic set
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Computing Small Certificates of Inconsistency of Quadratic Fewnomial Systems
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Critical Point Computations on Smooth Varieties
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New results on quantifier elimination over real closed fields and applications to constraint databases
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Reachability and connectivity queries in constraint databases
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Computing the Connected Components of Real Algebraic Curves
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Tracing-problems in dynamic geometry
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Numerically computing real points on algebraic sets
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Algorithms in Real Algebraic Geometry: A Survey
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Counting complexity classes for numeric computations II: algebraic and semialgebraic sets
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Computing the First Betti Numberand Describing the Connected Components of Semi-algebraic Sets
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Modeling and qualitative simulation of hybrid systems
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Exact algorithms for determinantal varieties and semidefinite programming
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