On the public citation graph

The complexity and construction of many faces in arrangements of lines and of segments

https://doi.org/10.1007/bf02187784
0 signed · 125 inferred · view as graph

Inferred edges come from two machine sources: sweeps of open repository metadata (mostly SSRN and Zenodo), and a bulk OpenAlex citation snapshot. Every row below is labelled with the one it came from. Neither is a complete citation index — absence here is not evidence of absence.

Is this your work? Sign in with ORCID and put your name on the claims that are yours.
Claim with ORCID
Reference health. See whether every reference in this work resolves to a known work and none has been retracted — and get a dated CiteStamped badge you can embed.
See reference health

What this work says

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

inferredcites →https://doi.org/10.1007/978-1-4612-1098-6openalex-snapshot
Computational Geometry
inferredcites →https://doi.org/10.1007/978-1-4612-9906-6openalex-snapshot
Geometric Topology in Dimensions 2 and 3
inferredcites →https://doi.org/10.1007/978-3-642-61568-9openalex-snapshot
Algorithms in Combinatorial Geometry
inferredcites →https://doi.org/10.1007/978-3-642-83539-1_42openalex-snapshot
Ray Tracing Algorithms — Theory and Practice
inferredcites →https://doi.org/10.1007/bf02187742openalex-snapshot
Implicitly representing arrangements of lines or segments
inferredcites →https://doi.org/10.1007/bf02187744openalex-snapshot
On the general motion-planning problem with two degrees of freedom
inferredcites →https://doi.org/10.1007/bf02187778openalex-snapshot
The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2
inferredcites →https://doi.org/10.1007/bf02187783openalex-snapshot
Combinatorial complexity bounds for arrangements of curves and spheres
inferredcites →https://doi.org/10.1007/bf02187785openalex-snapshot
The complexity of many cells in arrangements of planes and related problems
inferredcites →https://doi.org/10.1007/bf02187805openalex-snapshot
Partitioning arrangements of lines I: An efficient deterministic algorithm
inferredcites →https://doi.org/10.1007/bf02187876openalex-snapshot
ɛ-nets and simplex range queries
inferredcites →https://doi.org/10.1007/bf02187879openalex-snapshot
New applications of random sampling in computational geometry
inferredcites →https://doi.org/10.1007/bf02187894openalex-snapshot
Planar realizations of nonlinear davenport-schinzel sequences by segments
inferredcites →https://doi.org/10.1007/bf02187902openalex-snapshot
Separating two simple polygons by a sequence of translations
inferredcites →https://doi.org/10.1007/bf02579170openalex-snapshot
Nonlinearity of davenport—Schinzel sequences and of generalized path compression schemes
inferredcites →https://doi.org/10.1007/bf02579194openalex-snapshot
Extremal problems in discrete geometry
inferredcites →https://doi.org/10.1007/bf02788872openalex-snapshot
A theorem on arrangements of lines in the plane
inferredcites →https://doi.org/10.1016/0020-0190(86)90088-8openalex-snapshot
Halfplanar range search in linear space and O(n0.695) query time
inferredcites →https://doi.org/10.1016/0097-3165(86)90078-6openalex-snapshot
On the maximal number of edges of many faces in an arrangement
inferredcites →https://doi.org/10.1109/sfcs.1988.21973openalex-snapshot
Combinatorial complexity bounds for arrangements of curves and surfaces
inferredcites →https://doi.org/10.1109/tc.1979.1675432openalex-snapshot
Algorithms for Reporting and Counting Geometric Intersections
inferredcites →https://doi.org/10.1137/0215003openalex-snapshot
The Signature of a Plane Curve
inferredcites →https://doi.org/10.1137/0215023openalex-snapshot
Optimal Point Location in a Monotone Subdivision
inferredcites →https://doi.org/10.1137/0215024openalex-snapshot
Constructing Arrangements of Lines and Hyperplanes with Applications
inferredcites →https://doi.org/10.1137/0216005openalex-snapshot
On k -Hulls and Related Problems
inferredcites →https://doi.org/10.1145/73393.73394openalex-snapshot
Applications of random sampling in computational geometry, II
inferredcites →https://doi.org/10.1145/73393.73423openalex-snapshot
On the general motion planning problem with two degrees of freedom
inferredcites →https://doi.org/10.1145/73393.73432openalex-snapshot
Triangles in space or building (and analyzing) castles in the Air
inferredcites →https://doi.org/10.1145/73833.73835openalex-snapshot
A deterministic algorithm for partitioning arrangements of lines and its application
inferredcites →https://doi.org/10.1145/7531.24036openalex-snapshot
Intersection of convex objects in two and three dimensions
inferredcites →https://doi.org/10.2307/2008200openalex-snapshot
Computational Geometry--An Introduction.
inferredcites →https://doi.org/10.2307/2325168openalex-snapshot
Algorithms in Combinatorial Geometry.

What points at this work

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

inferred← citeshttps://doi.org/10.1006/jagm.1993.1020openalex-snapshot
Convex Hulls for Random Lines
inferred← citeshttps://doi.org/10.1007/0-387-25036-0_11openalex-snapshot
Incidences
inferred← citeshttps://doi.org/10.1007/3-540-19488-6_118openalex-snapshot
Arrangements of curves in the plane — topology, combinatorics, and algorithms
inferred← citeshttps://doi.org/10.1007/3-540-52921-7_93openalex-snapshot
Weaving patterns of lines and line segments in space
inferred← citeshttps://doi.org/10.1007/3-540-55719-9_94openalex-snapshot
A tail estimate for Mulmuley's segment intersection algorithm
inferred← citeshttps://doi.org/10.1007/3-540-57155-8_281openalex-snapshot
Combinatorial complexity of signed discs
inferred← citeshttps://doi.org/10.1007/3-540-57568-5_229openalex-snapshot
Reaching a goal with directional uncertainty
inferred← citeshttps://doi.org/10.1007/3-540-61422-2_139openalex-snapshot
Visibility with multiple reflections
inferred← citeshttps://doi.org/10.1007/978-0-387-87363-3_2openalex-snapshot
Computing the Detour and Spanning Ratio of Paths, Trees, and Cycles
inferred← citeshttps://doi.org/10.1007/978-3-642-55566-4_1openalex-snapshot
On the Complexity of Many Faces in Arrangements of Pseudo-Segments and Circles
inferred← citeshttps://doi.org/10.1007/978-3-642-58043-7_2openalex-snapshot
Combinatorics and Algorithms of Arrangements
inferred← citeshttps://doi.org/10.1007/978-3-642-58043-7_4openalex-snapshot
Epsilon-Nets and Computational Geometry
inferred← citeshttps://doi.org/10.1007/978-3-642-83539-1_9openalex-snapshot
Davenport-Schinzel Sequences and their Geometric Applications
inferred← citeshttps://doi.org/10.1007/bf01258293openalex-snapshot
Robot motion planning and the single cell problem in arrangements
inferred← citeshttps://doi.org/10.1007/bf01285815openalex-snapshot
The number of edges of many faces in a line segment arrangement
inferred← citeshttps://doi.org/10.1007/bf01293267openalex-snapshot
An improved technique for output-sensitive hidden surface removal
inferred← citeshttps://doi.org/10.1007/bf01758854openalex-snapshot
Quasi-optimal upper bounds for simplex range searching and new zone theorems
inferred← citeshttps://doi.org/10.1007/bf01758855openalex-snapshot
Minimum-link paths among obstacles in the plane
inferred← citeshttps://doi.org/10.1007/bf02123007openalex-snapshot
Triangles in space or building (and analyzing) castles in the air
inferred← citeshttps://doi.org/10.1007/bf02187783openalex-snapshot
Combinatorial complexity bounds for arrangements of curves and spheres
inferred← citeshttps://doi.org/10.1007/bf02187805openalex-snapshot
Partitioning arrangements of lines I: An efficient deterministic algorithm
inferred← citeshttps://doi.org/10.1007/bf02187809openalex-snapshot
Partitioning arrangements of lines II: Applications
inferred← citeshttps://doi.org/10.1007/bf02573992openalex-snapshot
On the complexity of a single cell in certain arrangements of surfaces related to motion planning
inferred← citeshttps://doi.org/10.1007/bf02574043openalex-snapshot
Arrangements of segments that share endpoints: Single face results
inferred← citeshttps://doi.org/10.1007/bf02574371openalex-snapshot
Castles in the air revisited
inferred← citeshttps://doi.org/10.1007/bf02574376openalex-snapshot
On lines missing polyhedral sets in 3-space
inferred← citeshttps://doi.org/10.1007/bf02712875openalex-snapshot
New lower bounds for Hopcroft's problem
inferred← citeshttps://doi.org/10.1007/bfb0009479openalex-snapshot
Separating and shattering long line segments
inferred← citeshttps://doi.org/10.1007/bfb0038185openalex-snapshot
On the zone theorem for hyperplane arrangements
inferred← citeshttps://doi.org/10.1007/pl00009378openalex-snapshot
Visibility with Multiple Reflections
inferred← citeshttps://doi.org/10.1007/pl00009396openalex-snapshot
Geometric Lower Bounds for Parametric Matroid Optimization
inferred← citeshttps://doi.org/10.1007/s00453-001-0096-5openalex-snapshot
Efficiently Approximating Polygonal Paths in Three and Higher Dimensions
inferred← citeshttps://doi.org/10.1007/s00454-003-0854-zopenalex-snapshot
Cell Complexities in Hyperplane Arrangements
inferred← citeshttps://doi.org/10.1007/s00454-007-9019-9openalex-snapshot
Computing the Detour and Spanning Ratio of Paths, Trees, and Cycles in 2D and 3D
inferred← citeshttps://doi.org/10.1016/0020-0190(96)00065-8openalex-snapshot
Excess in arrangements of segments
inferred← citeshttps://doi.org/10.1016/0097-3165(89)90032-0openalex-snapshot
Sharp upper and lower bounds on the length of general Davenport-Schinzel sequences
inferred← citeshttps://doi.org/10.1016/0167-8655(91)90042-kopenalex-snapshot
A counterexample to a dynamic algorithm for convex hulls of line arrangements
inferred← citeshttps://doi.org/10.1016/0304-3975(94)00237-dopenalex-snapshot
Reaching a goal with directional uncertainty
inferred← citeshttps://doi.org/10.1016/0925-7721(91)90011-3openalex-snapshot
Merging visibility maps
inferred← citeshttps://doi.org/10.1016/0925-7721(92)90008-gopenalex-snapshot
Improved combinatorial bounds and efficient techniques for certain motion planning problems with three degrees of freedom
inferred← citeshttps://doi.org/10.1016/0925-7721(93)90018-2openalex-snapshot
On the union of fat wedges and separating a collection of segments by a line
inferred← citeshttps://doi.org/10.1016/0925-7721(94)00026-xopenalex-snapshot
Combinatorial complexity of signed discs
inferred← citeshttps://doi.org/10.1016/0925-7721(95)00022-2openalex-snapshot
On a class of O(n2) problems in computational geometry
inferred← citeshttps://doi.org/10.1016/b978-044482537-7/50002-4openalex-snapshot
Davenport–Schinzel Sequences and Their Geometric Applications**Both authors have been supported by a grant from the U.S.–Israeli Binational Science Foundation. Pankaj Agarwal has also been supported by a National Science Foundation Grant CCR-93–01259, by an Army Research Office MURI grant…
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.comgeo.2011.11.006openalex-snapshot
On a class of O(n2) problems in computational geometry
inferred← citeshttps://doi.org/10.1016/j.comgeo.2025.102196openalex-snapshot
Algorithms for computing closest points for segments
inferred← citeshttps://doi.org/10.1016/j.dam.2014.04.009openalex-snapshot
A note on visibility-constrained Voronoi diagrams
inferred← citeshttps://doi.org/10.1016/s0020-0190(97)00188-9openalex-snapshot
Separating and shattering long line segments
inferred← citeshttps://doi.org/10.1016/s0166-218x(01)00315-8openalex-snapshot
Shattering a set of objects in 2D
inferred← citeshttps://doi.org/10.1016/s0166-3615(98)00067-0openalex-snapshot
Optimal workpiece setups for 4-axis numerical control machining based on machinability
inferred← citeshttps://doi.org/10.1016/s0925-7721(96)00004-1openalex-snapshot
The common exterior of convex polygons in the plane
inferred← citeshttps://doi.org/10.1016/s0927-0507(05)80124-0openalex-snapshot
Chapter 7 A survey of computational geometry
inferred← citeshttps://doi.org/10.1109/12.376174openalex-snapshot
On computing connected components of line segments
inferred← citeshttps://doi.org/10.1109/sfcs.1988.21973openalex-snapshot
Combinatorial complexity bounds for arrangements of curves and surfaces
inferred← citeshttps://doi.org/10.1109/sfcs.1991.185347openalex-snapshot
Fat triangles determine linearly many holes (computational geometry)
inferred← citeshttps://doi.org/10.1109/sfcs.1993.366835openalex-snapshot
The union of convex polyhedra in three dimensions
inferred← citeshttps://doi.org/10.1109/sfcs.2000.892130openalex-snapshot
On the boundary complexity of the union of fat triangles
inferred← citeshttps://doi.org/10.1109/sfcs.2001.959882openalex-snapshot
On the complexity of many faces in arrangements of circles
inferred← citeshttps://doi.org/10.1109/sffcs.1999.814588openalex-snapshot
Efficient regular data structures and algorithms for location and proximity problems
inferred← citeshttps://doi.org/10.1115/1.3615687openalex-snapshot
On Minimum Link Monotone Path Problems
inferred← citeshttps://doi.org/10.1117/12.25506openalex-snapshot
Algorithmic approaches to optimal route planning
inferred← citeshttps://doi.org/10.1137/0222031openalex-snapshot
On the Zone Theorem for Hyperplane Arrangements
inferred← citeshttps://doi.org/10.1137/0222077openalex-snapshot
Computing a Face in an Arrangement of Line Segments and Related Problems
inferred← citeshttps://doi.org/10.1137/1.9781611977073.10openalex-snapshot
Hopcroft's Problem, Log-Star Shaving, 2D Fractional Cascading, and Decision Trees
inferred← citeshttps://doi.org/10.1137/1.9781611977073.123openalex-snapshot
Constructing Many Faces in Arrangements of Lines and Segments
inferred← citeshttps://doi.org/10.1137/120891241openalex-snapshot
Improved Bounds for the Union of Locally Fat Objects in the Plane
inferred← citeshttps://doi.org/10.1137/24m1640732openalex-snapshot
Covering Points by Hyperplanes and Related Problems
inferred← citeshttps://doi.org/10.1137/s0097539700382169openalex-snapshot
On the Boundary Complexity of the Union of Fat Triangles
inferred← citeshttps://doi.org/10.1137/s0097539703433900openalex-snapshot
Pseudo-Line Arrangements: Duality, Algorithms, and Applications
inferred← citeshttps://doi.org/10.1137/s009753979018330xopenalex-snapshot
Fat Triangles Determine Linearly Many Holes
inferred← citeshttps://doi.org/10.1137/s0097539792229404openalex-snapshot
On Collision-Free Placements of Simplices and the Closest Pair of Lines in 3-Space
inferred← citeshttps://doi.org/10.1137/s0097539793250755openalex-snapshot
The Union of Convex Polyhedra in Three Dimensions
inferred← citeshttps://doi.org/10.1137/s009753979426616xopenalex-snapshot
Computing Many Faces in Arrangements of Lines and Segments
inferred← citeshttps://doi.org/10.1142/s0218195901000456openalex-snapshot
REACHING A POLYGON WITH DIRECTIONAL UNCERTAINTY
inferred← citeshttps://doi.org/10.1145/109648.109670openalex-snapshot
The upper envelope of Voronoi surfaces and its applications
inferred← citeshttps://doi.org/10.1145/109648.109683openalex-snapshot
On the complexity of a single cell in certain arrangements of surfaces in 3-space (extended abstract)
inferred← citeshttps://doi.org/10.1145/109648.109684openalex-snapshot
Arrangements of segments that share endpoints
inferred← citeshttps://doi.org/10.1145/109648.109689openalex-snapshot
Triangulation and CSG representation of polyhedra with arbitrary genus
inferred← citeshttps://doi.org/10.1145/142675.142703openalex-snapshot
Incidence and nearest-neighbor problems for lines in 3-space
inferred← citeshttps://doi.org/10.1145/142675.142710openalex-snapshot
Castles in the air revisited
inferred← citeshttps://doi.org/10.1145/160985.160990openalex-snapshot
On lines missing polyhedral sets in 3-space
inferred← citeshttps://doi.org/10.1145/177424.177548openalex-snapshot
Computing many faces in arrangements of lines and segments
inferred← citeshttps://doi.org/10.1145/195058.195110openalex-snapshot
Computational geometry
inferred← citeshttps://doi.org/10.1145/220279.220293openalex-snapshot
New lower bounds for Hopcroft's problem
inferred← citeshttps://doi.org/10.1145/225058.225284openalex-snapshot
Geometric lower bounds for parametric matroid optimization
inferred← citeshttps://doi.org/10.1145/276884.276920openalex-snapshot
Efficiently approximating polygonal paths in three and higher dimensions
inferred← citeshttps://doi.org/10.1145/3591357openalex-snapshot
Hopcroft’s Problem, Log* Shaving, Two-dimensional Fractional Cascading, and Decision Trees
inferred← citeshttps://doi.org/10.1145/73393.73432openalex-snapshot
Triangles in space or building (and analyzing) castles in the Air
inferred← citeshttps://doi.org/10.1145/98524.98532openalex-snapshot
Quasi-optimal upper bounds for simplex range searching and new zone theorems
inferred← citeshttps://doi.org/10.1145/98524.98537openalex-snapshot
Minimum-link paths among obstacles in the plane
inferred← citeshttps://doi.org/10.1145/98524.98561openalex-snapshot
Merging visibility maps
inferred← citeshttps://doi.org/10.1201/9781439864524-22openalex-snapshot
Conv olution of polyhedral tracings
Editorial review for independent work. ICSAC — the Institute for Complexity Science and Advanced Computing — runs a structured editorial panel for researchers publishing outside journals, and publishes on CiteStamp rails. Submission is free and goes through ORCID: icsacinstitute.org/submit.