Making data structures persistent
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Topologically sweeping an arrangement
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
An efficient and simple motion planning algorithm for a ladder amidst polygonal barriers
Journal of Algorithms
Planar realizations of nonlinear Davenport-Schinzel sequences by segments
Discrete & Computational Geometry
Separating two simple polygons by a sequence of translations
Discrete & Computational Geometry
The complexity of many faces in arrangements of lines of segments
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
On arrangements of Jordan arcs with three intersections per pair
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Coordinated motion planning for two independent robots
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Triangles in space or building (and analyzing) castles in the Air
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Planning algorithm for a convex polygonal object in two-dimensional polygonal space
Discrete & Computational Geometry
SCG '85 Proceedings of the first annual symposium on Computational geometry
Visibility and intersectin problems in plane geometry
SCG '85 Proceedings of the first annual symposium on Computational geometry
An algorithm for planning collision-free paths among polyhedral obstacles
Communications of the ACM
Arrangements of Curves in the Plane - Topology, Combinatorics, and Algorithms
ICALP '88 Proceedings of the 15th International Colloquium on Automata, Languages and Programming
The complexity of many faces in arrangements of lines of segments
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Coordinated motion planning for two independent robots
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Efficient motion planning for an L-shaped object
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Compliant motion in a simple polygon
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Ray shooting and other applications of spanning trees with low stabbing number
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
On the two-dimensional davenport-schinzel problem
Journal of Symbolic Computation
Gross motion planning—a survey
ACM Computing Surveys (CSUR)
Incidence and nearest-neighbor problems for lines in 3-space
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
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We show that, under reasonable assumptions, any collision-avoiding motion planning problem for a moving system with two degrees of freedom can be solved in time &Ogr;(&lgr;s(n) log2n), where n is the number of collision constraints imposed on the system, s is a fixed parameter depending e.g. on the maximum algebraic degree of these constraints, and &lgr;s(n) is the (almost linear) maximum length of (n,s) Davenport Schinzel sequences. This follows from an upper bound of &Ogr;(&lgr;s(n)) that we establish for the combinatorial complexity of a single connected component of the space of all free placements of the moving system. Although our study is motivated by motion planning, it is actually a study of topological, combinatorial, and algorithmic issues involving a single face in an arrangement of curves. Our results thus extend beyond the area of motion planning, and have applications in many other areas.