On decomposing polygons into uniformly monotone parts
Information Processing Letters
On monotone paths among obstacles with applications to planning assemblies
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Minimum dissection of rectilinear polygon with arbitrary holes into rectangles
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Single-layer fanout routing and routability analysis for Ball Grid Arrays
ICCAD '95 Proceedings of the 1995 IEEE/ACM international conference on Computer-aided design
On finding non-intersecting paths in grids and its application in reconfiguring VLSI/WSI arrays
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Escaping a grid by edge-disjoint paths
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Efficient algorithms for finding the maximum number of disjoint paths in grids
Journal of Algorithms
Efficient Breakout Routing in Printed Circuit Boards (Extended Abstract)
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
Robotic Radiosurgery with Beams of Adaptable Shapes
CVRMed '95 Proceedings of the First International Conference on Computer Vision, Virtual Reality and Robotics in Medicine
Optimal Terrain Construction Problems and Applications in Intensity-Modulated Radiation Therapy
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Mountain reduction, block matching, and applications in intensity-modulated radiation therapy
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
The intensity level reduction in radiation therapy
Proceedings of the 2005 ACM symposium on Applied computing
Efficient intensity map splitting algorithms for intensity-modulated radiation therapy
Information Processing Letters
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
Efficient algorithms for intensity map splitting problems in radiation therapy
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Generalized geometric approaches for leaf sequencing problems in radiation therapy,
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Generalized geometric approaches for leaf sequencing problems in radiation therapy
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Field splitting problems in intensity-modulated radiation therapy
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
An almost linear time algorithm for field splitting in radiation therapy
Computational Geometry: Theory and Applications
| Hi-index | 0.00 |
The static leaf sequencing (SLS) problem arises in radiation therapy for cancer treatments, aiming to accomplish the delivery of a radiation prescription to a target tumor in the minimum amount of delivery time. Geometrically, the SLS problem can be formulated as a 3-D partition problem for which the 2-D problem of partitioning a polygonal domain (possibly with holes) into a minimum set of monotone polygons is a special case. In this paper, we present new geometric algorithms for a basic case of the 3-D SLS problem (which is also of clinical value) and for the general 3-D SLS problem. Our basic 3-D SLS algorithm, based on new geometric observations, produces guaranteed optimal quality solutions using Steiner points in polynomial time; the previously best known basic 3-D SLS algorithm gives optimal outputs only for the case without any Steiner points, and its time bound involves a multiplicative factor of a factorial function of the input. Our general 3-D SLS algorithm is based on our basic 3-D SLS algorithm and a polynomial time algorithm for partitioning a polygonal domain (possibly with holes) into a minimum set of x-monotone polygons, and has a fast running time. Experiments and comparisons using real medical data and on a real radiotherapy machine have shown that our 3-D SLS algorithms and software produce treatment plans that use significantly shorter delivery time and give better treatment quality than the current most popular commercial treatment planning system and the most well-known SLS algorithm. Some of our techniques and geometric procedures (e.g., for the problem of partitioning a polygonal domain into a minimum set of x-monotone polygons) are interesting in their own right.