Worst-case optimal algorithms for constructing visibility polygons with holes
SCG '86 Proceedings of the second annual symposium on Computational geometry
Efficient algorithms for geometric graph search problems
SIAM Journal on Computing
A linear time algorithm with minimum link paths inside a simple polygon
Computer Vision, Graphics, and Image Processing
Optimal computation of finitely oriented convex hulls
Information and Computation
Dynamic orthogonal segment intersection search
Journal of Algorithms
On some distance problems in fixed orientations
SIAM Journal on Computing
New algorithms for special cases of the hidden line elimination problem
Computer Vision, Graphics, and Image Processing
Quasi-optimal range searching in spaces of finite VC-dimension
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Computing the visibility polygon from a convex set and related problems
Journal of Algorithms
Computational Geometry: Theory and Applications
Computing minimum length paths of a given homotopy class
Computational Geometry: Theory and Applications
A pedestrian approach to ray shooting: shoot a ray, take a walk
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Rectilinear Path Problems Among Rectilinear ObstaclesRevisited
SIAM Journal on Computing
On a class of O(n2) problems in computational geometry
Computational Geometry: Theory and Applications
Rectilinear paths among rectilinear obstacles
Discrete Applied Mathematics
Selected papers from the 12th annual symposium on Computational Geometry
On Bends and Distances of Paths Among Obstacles in Two-Layer Interconnection Model
IEEE Transactions on Computers
Line Simplification with Restricted Orientations
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
On Spanning Trees with Low Crossing Numbers
Data Structures and Efficient Algorithms, Final Report on the DFG Special Joint Initiative
On approximate halfspace range counting and relative epsilon-approximations
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Dynamic Segment Intersection Search With Applications
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
Faster algorithms for minimum-link paths with restricted orientations
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Discrete & Computational Geometry
| Hi-index | 0.00 |
A path or a polygonal domain is C-oriented if the orientations of its edges belong to a set of C given orientations; this is a generalization of the notable rectilinear case (C=2). We study exact and approximation algorithms for minimum-link C-oriented paths and paths with unrestricted orientations, both in C-oriented and in general domains. Our two main algorithms are as follows:A subquadratic-time algorithm with a non-trivial approximation guarantee for general (unrestricted-orientation) minimum-link paths in general domains. An algorithm to find a minimum-link C-oriented path in a C-oriented domain. Our algorithm is simpler and more time-space efficient than the prior algorithm. We also obtain several related results:*3SUM-hardness of determining the link distance with unrestricted orientations (even in a rectilinear domain). *An optimal algorithm for finding a minimum-link rectilinear path in a rectilinear domain. The algorithm and its analysis are simpler than the existing ones. *An extension of our methods to find a C-oriented minimum-link path in a general (not necessarily C-oriented) domain. *A more efficient algorithm to compute a 2-approximate C-oriented minimum-link path. *A notion of ''robust'' paths. We show how minimum-link C-oriented paths approximate the robust paths with unrestricted orientations to within an additive error of 1.