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A Nearly Optimal Algorithm for Deciding Connectivity Queries in Smooth and Bounded Real 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/10.1006/jcom.1997.0432openalex-snapshot
Polar Varieties, Real Equation Solving, and Data Structures: The Hypersurface Case
inferredcites →https://doi.org/10.1006/jcom.2000.0563openalex-snapshot
Finding at Least One Point in Each Connected Component of a Real Algebraic Set Defined by a Single Equation
inferredcites →https://doi.org/10.1006/jcom.2000.0571openalex-snapshot
A Gröbner Free Alternative for Polynomial System Solving
inferredcites →https://doi.org/10.1006/jsco.2002.0563openalex-snapshot
Real Solving for Positive Dimensional Systems
inferredcites →https://doi.org/10.1007/3-540-15984-3_279openalex-snapshot
About a new method for computing in algebraic number fields
inferredcites →https://doi.org/10.1007/3-540-28296-3openalex-snapshot
Computational Commutative Algebra 2
inferredcites →https://doi.org/10.1007/3-540-33099-2openalex-snapshot
Algorithms in Real Algebraic Geometry
inferredcites →https://doi.org/10.1007/3-540-60114-7_16openalex-snapshot
When polynomial equation systems can be “solved” fast?
inferredcites →https://doi.org/10.1007/978-0-387-35651-8openalex-snapshot
Ideals, Varieties, and Algorithms
inferredcites →https://doi.org/10.1007/978-1-4612-0913-3openalex-snapshot
Gröbner Bases: A Computational Approach to Commutative Algebra
inferredcites →https://doi.org/10.1007/978-3-0348-9104-2_1openalex-snapshot
Zeros, multiplicities, and idempotents for zero-dimensional systems
inferredcites →https://doi.org/10.1007/978-3-642-38010-5openalex-snapshot
Basic Algebraic Geometry 2
inferredcites →https://doi.org/10.1007/978-3-642-57956-1openalex-snapshot
Basic Algebraic Geometry 2
inferredcites →https://doi.org/10.1007/978-3-642-61833-8openalex-snapshot
Algebraic Geometry I Complex Projective Varieties
inferredcites →https://doi.org/10.1007/bf01200148openalex-snapshot
Construction of roadmaps in semi-algebraic sets
inferredcites →https://doi.org/10.1007/pl00004896openalex-snapshot
Polar varieties and efficient real elimination
inferredcites →https://doi.org/10.1007/s00200-002-0109-xopenalex-snapshot
Computing Parametric Geometric Resolutions
inferredcites →https://doi.org/10.1007/s00200-009-0117-1openalex-snapshot
On the geometry of polar varieties
inferredcites →https://doi.org/10.1007/s002000050114openalex-snapshot
Solving Zero-Dimensional Systems Through the Rational Univariate Representation
inferredcites →https://doi.org/10.1007/s00454-009-9239-2openalex-snapshot
A Baby Steps/Giant Steps Probabilistic Algorithm for Computing Roadmaps in Smooth Bounded Real Hypersurface
inferredcites →https://doi.org/10.1007/s00454-014-9610-9openalex-snapshot
Divide and Conquer Roadmap for Algebraic Sets
inferredcites →https://doi.org/10.1007/s10208-014-9212-1openalex-snapshot
A Baby Step–Giant Step Roadmap Algorithm for General Algebraic Sets
inferredcites →https://doi.org/10.1007/s10208-014-9214-zopenalex-snapshot
Degeneracy Loci and Polynomial Equation Solving
inferredcites →https://doi.org/10.1016/0096-3003(87)90063-4openalex-snapshot
A homotopy for solving general polynomial systems that respects m-homogeneous structures
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/10.1016/0304-3975(83)90110-xopenalex-snapshot
The complexity of partial derivatives
inferredcites →https://doi.org/10.1016/1385-7258(78)90048-3openalex-snapshot
On varieties in multiple-projective spaces
inferredcites →https://doi.org/10.1016/j.exmath.2007.07.001openalex-snapshot
A concise proof of the Kronecker polynomial system solver from scratch
inferredcites →https://doi.org/10.1016/j.jco.2004.10.001openalex-snapshot
Generalized polar varieties: geometry and algorithms
inferredcites →https://doi.org/10.1016/j.jco.2014.02.005openalex-snapshot
Intrinsic complexity estimates in polynomial optimization
inferredcites →https://doi.org/10.1016/j.jsc.2012.05.008openalex-snapshot
On the complexity of computing with zero-dimensional triangular sets
inferredcites →https://doi.org/10.1016/j.tcs.2007.10.003openalex-snapshot
Change of order for regular chains in positive dimension
inferredcites →https://doi.org/10.1016/s0022-4049(96)00099-0openalex-snapshot
Straight-line programs in geometric elimination theory
inferredcites →https://doi.org/10.1016/s0024-3795(02)00471-8openalex-snapshot
Inversion of two level circulant matrices over Zp
inferredcites →https://doi.org/10.1016/s0764-4442(97)83558-6openalex-snapshot
Le rôle des structures de données dans les problèmes d'élimination
inferredcites →https://doi.org/10.1017/cbo9780511546877openalex-snapshot
Planning Algorithms
inferredcites →https://doi.org/10.1090/s0894-0347-99-00311-2openalex-snapshot
Computing roadmaps of semi-algebraic sets on a variety
inferredcites →https://doi.org/10.1093/comjnl/36.5.504openalex-snapshot
Computing Roadmaps of General Semi-Algebraic Sets
inferredcites →https://doi.org/10.1098/rspa.1962.0170openalex-snapshot
Ideals defined by matrices and a certain complex associated with them
inferredcites →https://doi.org/10.1109/tac.1977.1101627openalex-snapshot
The numerical solution of A'Q+QA = -C
inferredcites →https://doi.org/10.1137/130931308openalex-snapshot
Probabilistic Algorithm for Polynomial Optimization over a Real Algebraic Set
inferredcites →https://doi.org/10.1142/5763openalex-snapshot
The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
inferredcites →https://doi.org/10.1145/1113439.1113457openalex-snapshot
On the complexity of the D5 principle
inferredcites →https://doi.org/10.1145/1145768.1145814openalex-snapshot
Change of order for bivariate triangular sets
inferredcites →https://doi.org/10.1145/237814.237857openalex-snapshot
Computing roadmaps of semi-algebraic sets (extended abstract)
inferredcites →https://doi.org/10.1145/345542.345633openalex-snapshot
Computing an equidimensional decomposition of an algebraic variety by means of geometric resolutions
inferredcites →https://doi.org/10.1145/800141.804674openalex-snapshot
Testing polynomials which are easy to compute (Extended Abstract)
inferredcites →https://doi.org/10.1145/860854.860901openalex-snapshot
Polar varieties and computation of one point in each connected component of a smooth real algebraic set
inferredcites →https://doi.org/10.1515/9783112342404-001openalex-snapshot
Grundzüge einer arithmetischen Theorie der algebraischen Grössen
inferredcites →https://doi.org/10.2307/1970783openalex-snapshot
Generic Projections
inferredcites →https://doi.org/10.24033/asens.1346openalex-snapshot
Polar classes of singular varieties
inferredcites →https://doi.org/10.3792/chmm/1263317740openalex-snapshot
The algebraic theory of modular systems
inferredcites →https://doi.org/10.5860/choice.33-4552openalex-snapshot
Commutative algebra with a view toward algebraic geometry

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.1007/978-3-031-91095-1_11openalex-snapshot
Singular Points of UOV and VOX
inferred← citeshttps://doi.org/10.1007/s00200-019-00396-wopenalex-snapshot
Real root finding for low rank linear matrices
inferred← citeshttps://doi.org/10.1007/s10208-018-9392-1openalex-snapshot
Improved Complexity Bounds for Counting Points on Hyperelliptic Curves
inferred← citeshttps://doi.org/10.1007/s10208-022-09599-zopenalex-snapshot
Counting Real Roots in Polynomial-Time via Diophantine Approximation
inferred← citeshttps://doi.org/10.1007/s10957-025-02788-0openalex-snapshot
Univariate Representations of Solutions to Generic Polynomial Complementarity Problems
inferred← citeshttps://doi.org/10.1007/s11424-023-2119-7openalex-snapshot
On Types of Isolated KKT Points in Polynomial Optimization
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.2022.03.002openalex-snapshot
Gröbner bases and critical values: The asymptotic combinatorics of determinantal systems
inferred← citeshttps://doi.org/10.1016/j.jalgebra.2025.01.014openalex-snapshot
On the arithmetic complexity of computing Gröbner bases of comaximal determinantal ideals
inferred← citeshttps://doi.org/10.1016/j.jalgebra.2025.03.053openalex-snapshot
Generic consistency and nondegeneracy of vertically parametrized systems
inferred← citeshttps://doi.org/10.1016/j.jco.2019.101440openalex-snapshot
Counting points on hyperelliptic curves with explicit real multiplication in arbitrary genus
inferred← citeshttps://doi.org/10.1016/j.jco.2021.101557openalex-snapshot
Homotopy techniques for solving sparse column support determinantal polynomial systems
inferred← citeshttps://doi.org/10.1016/j.jsc.2015.06.010openalex-snapshot
Real root finding for determinants of linear matrices
inferred← citeshttps://doi.org/10.1016/j.jsc.2017.07.009openalex-snapshot
Solving rank-constrained semidefinite programs in exact arithmetic
inferred← citeshttps://doi.org/10.1016/j.jsc.2017.08.001openalex-snapshot
Bit complexity for multi-homogeneous polynomial system solving—Application to polynomial minimization
inferred← citeshttps://doi.org/10.1016/j.jsc.2019.03.004openalex-snapshot
On types of degenerate critical points of real polynomial functions
inferred← citeshttps://doi.org/10.1016/j.jsc.2019.10.018openalex-snapshot
Computing real radicals and S-radicals of polynomial systems
inferred← citeshttps://doi.org/10.1016/j.jsc.2020.04.006openalex-snapshot
Foreword
inferred← citeshttps://doi.org/10.1016/j.jsc.2020.09.008openalex-snapshot
Solving determinantal systems using homotopy techniques
inferred← citeshttps://doi.org/10.1016/j.jsc.2020.11.001openalex-snapshot
Exact Algorithms for Semidefinite Programs with Degenerate Feasible Set
inferred← citeshttps://doi.org/10.1016/j.jsc.2021.03.005openalex-snapshot
On exact Reznick, Hilbert-Artin and Putinar's representations
inferred← citeshttps://doi.org/10.1016/j.jsc.2021.12.002openalex-snapshot
Solving parametric systems of polynomial equations over the reals through Hermite matrices
inferred← citeshttps://doi.org/10.1016/j.jsc.2022.08.008openalex-snapshot
Positive dimensional parametric polynomial systems, connectivity queries and applications in robotics
inferred← citeshttps://doi.org/10.1016/j.jsc.2022.08.010openalex-snapshot
Bit complexity for computing one point in each connected component of a smooth real algebraic set
inferred← citeshttps://doi.org/10.1016/j.jsc.2022.10.002openalex-snapshot
Computing critical points for invariant algebraic systems
inferred← citeshttps://doi.org/10.1016/j.jsc.2023.102234openalex-snapshot
Computing roadmaps in unbounded smooth real algebraic sets I: Connectivity results
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/j.mechmachtheory.2020.104002openalex-snapshot
Variational path optimization of linear pentapods with a simple singularity variety
inferred← citeshttps://doi.org/10.1016/j.tcs.2017.03.035openalex-snapshot
Computing real witness points of positive dimensional polynomial systems
inferred← citeshttps://doi.org/10.1109/cdc.2014.7040227openalex-snapshot
NUROA: A numerical roadmap algorithm
inferred← citeshttps://doi.org/10.1134/s0965542520010121openalex-snapshot
Symmetric Matrices Whose Entries Are Linear Functions
inferred← citeshttps://doi.org/10.1137/130936294openalex-snapshot
On the Complexity of Computing Critical Points with Gröbner Bases
inferred← citeshttps://doi.org/10.1137/15m1009871openalex-snapshot
A Note on Polynomial Solvability of the CDT Problem
inferred← citeshttps://doi.org/10.1137/15m1036543openalex-snapshot
Exact Algorithms for Linear Matrix Inequalities
inferred← citeshttps://doi.org/10.1137/21m1436373openalex-snapshot
A Geometric Approach for Analyzing Parametric Biological Systems by Exploiting Block Triangular Structure
inferred← citeshttps://doi.org/10.1145/2755996.2756667openalex-snapshot
Real Root Finding for Rank Defects in Linear Hankel Matrices
inferred← citeshttps://doi.org/10.1145/2755996.2756670openalex-snapshot
Probabilistic Algorithm for Computing the Dimension of Real Algebraic Sets
inferred← citeshttps://doi.org/10.1145/2930889.2930925openalex-snapshot
Solving Rank-Constrained Semidefinite Programs in Exact Arithmetic
inferred← citeshttps://doi.org/10.1145/2930889.2930927openalex-snapshot
Computing Small Certificates of Inconsistency of Quadratic Fewnomial Systems
inferred← citeshttps://doi.org/10.1145/2930889.2930929openalex-snapshot
Critical Point Computations on Smooth Varieties
inferred← citeshttps://doi.org/10.1145/3208976.3209002openalex-snapshot
On the Complexity of Computing Real Radicals of Polynomial Systems
inferred← citeshttps://doi.org/10.1145/3208976.3209023openalex-snapshot
Real Root Finding for Equivariant Semi-algebraic Systems
inferred← citeshttps://doi.org/10.1145/3275242openalex-snapshot
Computing the Homology of Basic Semialgebraic Sets in Weak Exponential Time
inferred← citeshttps://doi.org/10.1145/3326229.3326262openalex-snapshot
Computing the Volume of Compact Semi-Algebraic Sets
inferred← citeshttps://doi.org/10.1145/3373207.3404049openalex-snapshot
Computing the real isolated points of an algebraic hypersurface
inferred← citeshttps://doi.org/10.1145/3373207.3404058openalex-snapshot
On the bit complexity of finding points in connected components of a smooth real hypersurface
inferred← citeshttps://doi.org/10.1145/3377006.3377014openalex-snapshot
Bit complexity for critical point computation in smooth and compact real hypersurfaces
inferred← citeshttps://doi.org/10.1145/3452143.3465546openalex-snapshot
Faster One Block Quantifier Elimination for Regular Polynomial Systems of Equations
inferred← citeshttps://doi.org/10.1145/3476446.3535471openalex-snapshot
Algorithms for Discrete Differential Equations of Order 1
inferred← citeshttps://doi.org/10.1145/3476446.3535477openalex-snapshot
Deciding Cuspidality of Manipulators through Computer Algebra and Algorithms in Real Algebraic Geometry
inferred← citeshttps://doi.org/10.1145/3476446.3536181openalex-snapshot
Computing Critical Points for Algebraic Systems Defined by Hyperoctahedral Invariant Polynomials
inferred← citeshttps://doi.org/10.1145/3476446.3536182openalex-snapshot
Finer Complexity Estimates for the Change of Ordering of Gröbner Bases for Generic Symmetric Determinantal Ideals
inferred← citeshttps://doi.org/10.1145/3597066.3597077openalex-snapshot
Refined F5 Algorithms for Ideals of Minors of Square Matrices
inferred← citeshttps://doi.org/10.1145/3597066.3597081openalex-snapshot
Algorithm for Connectivity Queries on Real Algebraic Curves
inferred← citeshttps://doi.org/10.1145/3597066.3597103openalex-snapshot
Fast Algorithms for Discrete Differential Equations
inferred← citeshttps://doi.org/10.1145/3666000.3669687openalex-snapshot
Connectivity in Symmetric Semi-Algebraic Sets
inferred← citeshttps://doi.org/10.1145/3666000.3669713openalex-snapshot
Optimized Gröbner basis algorithms for maximal determinantal ideals and critical point computations
inferred← citeshttps://doi.org/10.1145/3747199.3747570openalex-snapshot
Solving generic parametric linear matrix inequalities
inferred← citeshttps://doi.org/10.1145/3747199.3747572openalex-snapshot
Computing Polynomial Representation in Subrings of Multivariate Polynomial Rings
inferred← citeshttps://doi.org/10.1145/3815436.3815466openalex-snapshot
Computing the Connected Components of Real Algebraic Curves
inferred← citeshttps://doi.org/10.13140/rg.2.1.3525.2884openalex-snapshot
Solving rank-constrained semidefinite programs in exact arithmetic
inferred← citeshttps://doi.org/10.48550/arxiv.1406.6429openalex-snapshot
A note on polynomial solvability of the CDT problem
inferred← citeshttps://doi.org/10.48550/arxiv.1412.5873openalex-snapshot
Real root finding for determinants of linear matrices
inferred← citeshttps://doi.org/10.48550/arxiv.1502.02473openalex-snapshot
Real root finding for rank defects in linear Hankel matrices
inferred← citeshttps://doi.org/10.48550/arxiv.1710.03448openalex-snapshot
Improved Complexity Bounds for Counting Points on Hyperelliptic Curves
inferred← citeshttps://doi.org/10.48550/arxiv.1904.11705openalex-snapshot
Computing the volume of compact semi-algebraic sets
inferred← citeshttps://doi.org/10.48550/arxiv.2004.12315openalex-snapshot
On types of KKT points in polynomial optimization
inferred← citeshttps://doi.org/10.70675/2a76e51fz3424z4dd3zbed1z94f95e805983openalex-snapshot
Exact Algorithms for Polynomial Optimisation
inferred← citeshttps://doi.org/10.70675/539fc8c8zf4dfz4b29z9a8ez1a8673a3d9b4openalex-snapshot
On solving parametric polynomial systems and quantifier elimination over the reals : algorithms, complexity and implementations
inferred← citeshttps://doi.org/10.70675/64ae50fez53b8z4152zb19fz8380fc8e40d6openalex-snapshot
Counting points on hyperelliptic curves in large characteristic : algorithms and complexity
inferred← citeshttps://doi.org/10.70675/d0b760d0z6de6z48cazb255zb7c4e16724ecopenalex-snapshot
Homotopy algorithms for solving structured determinantal systems
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