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Approximate motion planning and the complexity of the boundary of the union of simple geometric figures
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
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Davenport-Schinzel Sequences and their Geometric Applications
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On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
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On the general motion-planning problem with two degrees of freedom
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An efficient motion-planning algorithm for a convex polygonal object in two-dimensional polygonal space
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Planning a purely translational motion for a convex object in two-dimensional space using generalized Voronoi diagrams
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Optimal Point Location in a Monotone Subdivision
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An efficient algorithm for planning collision-free translational motion of a convex polygonal object in 2-dimensional space amidst polygonal obstacles
inferredcites →https://doi.org/10.1145/73833.73853openalex-snapshot
Placing the largest similar copy of a convex polygon among polygonal obstacles
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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Differentially constrained mobile robot motion planning in state lattices
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Range Searching and Point Location among Fat Objects
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Realistic Environment Models and Their Impact on the Exact Solution of the Motion Planning Problem
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Improved Bounds on the Union Complexity of Fat Objects
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TSP with Neighborhoods of Varying Size
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Selected topics from computational geometry, data structures and motion planning
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Two- and three- dimensional point location in rectangular subdivisions
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Computing depth orders and related problems
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Dynamic data structures for fat objects and their applications
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Finding the Safest One-Dimensional Path among Obstacles for the Acceleration Constrained Robot
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The complexity of the free space for motion planning amidst fat obstacles
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On simultaneous inner and outer approximation of shapes
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Onk-sets in arrangements of curves and surfaces
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Range searching and point location among fat objects
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Motion Planning in Environments with Low Obstacle Density
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On the Complexity of the Union of Fat Convex Objects in the Plane
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Realistic Input Models for Geometric Algorithms
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Geometric Eccentricity and the Complexity of Manipulation Plans
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The Union of Congruent Cubes in Three Dimensions
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On the Union of κ-Round Objects in Three and Four Dimensions
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Improved Bounds on the Union Complexity of Fat Objects
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An Optimal-Time Algorithm for Shortest Paths on Realistic Polyhedra
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Pipes, Cigars, and Kreplach: the Union of Minkowski Sums in Three Dimensions
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The complexity of the free space for a robot moving amidst fat obstacles
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
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Computing depth orders for fat objects and related problems
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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Exact and approximation algorithms for computing optimal fat decompositions
inferred← citeshttps://doi.org/10.1016/j.comgeo.2007.10.003openalex-snapshot
Reporting flock patterns
inferred← citeshttps://doi.org/10.1016/j.jalgor.2005.01.010openalex-snapshot
TSP with neighborhoods of varying size
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On the fatness of Minkowski sums
inferred← citeshttps://doi.org/10.1016/s0925-7721(01)00022-0openalex-snapshot
Models and motion planning
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On fat partitioning, fat covering and the union size of polygons
inferred← citeshttps://doi.org/10.1016/s0925-7721(96)00027-2openalex-snapshot
3-D vertical ray shooting and 2-D point enclosure, range searching, and arc shooting amidst convex fat objects
inferred← citeshttps://doi.org/10.1017/cbo9780511546877.008openalex-snapshot
Combinatorial Motion Planning
inferred← citeshttps://doi.org/10.1080/00207169808804743openalex-snapshot
Visibility of rectagular objects inL1metric
inferred← citeshttps://doi.org/10.1090/conm/453/08794openalex-snapshot
State of the union (of geometric objects)
inferred← citeshttps://doi.org/10.1109/icra55743.2025.11127599openalex-snapshot
Asymptotically-Optimal Multi-Query Path Planning for a Polygonal Robot
inferred← citeshttps://doi.org/10.1109/robot.1993.291998openalex-snapshot
Efficient algorithms for exact motion planning amidst fat obstacles
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Planning paths of minimal curvature
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Fat triangles determine linearly many holes (computational geometry)
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/tase.2015.2470096openalex-snapshot
Efficient Multi-Robot Motion Planning for Unlabeled Discs in Simple Polygons
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Improved Bounds for the Union of Locally Fat Objects in the Plane
inferred← citeshttps://doi.org/10.1137/s0097539700382169openalex-snapshot
On the Boundary Complexity of the Union of Fat Triangles
inferred← citeshttps://doi.org/10.1137/s009753979018330xopenalex-snapshot
Fat Triangles Determine Linearly Many Holes
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EFFICIENT EXACT MOTION PLANNING IN REALISTIC ENVIRONMENTS
inferred← citeshttps://doi.org/10.1145/1247069.1247081openalex-snapshot
Shortest paths on realistic polyhedra
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Motion planning amidst fat obstacles (extended abstract)
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Better bounds on the union complexity of locally fat objects
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On fence design and the complexity of push plans for orienting parts
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Realistic input models for geometric algorithms
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On the union of κ-curved objects
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The union of congruent cubes in three dimensions
inferred← citeshttps://doi.org/10.1145/997817.997875openalex-snapshot
On the union of κ-round objects
inferred← citeshttps://doi.org/10.37236/6792openalex-snapshot
On the Union Complexity of Families of Axis-Parallel Rectangles with a Low Packing Number
inferred← citeshttps://doi.org/10.48550/arxiv.1702.00849openalex-snapshot
On the union complexity of families of axis-parallel rectangles with a low packing number
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Construction and Analysis of Geometric Networks
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Realistic analysis for algorithmic problems on geographical data
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