A faster approximation algorithm for the Steiner problem in graphs
Acta Informatica
Optimal point location in a monotone subdivision
SIAM Journal on Computing
An O(n log n) Algorithm for Rectilinear Minimal Spanning Trees
Journal of the ACM (JACM)
Two-Dimensional Voronoi Diagrams in the Lp-Metric
Journal of the ACM (JACM)
Rectilinear shortest paths with rectangular barriers
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
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Proximity and reachability in the plane.
Proximity and reachability in the plane.
Algorithms for Reporting and Counting Geometric Intersections
IEEE Transactions on Computers
Visibility-polygon search and euclidean shortest paths
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Parallel rectilinear shortest paths with rectangular obstacles
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Shortest rectilinear paths among weighted obstacles
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
A hardware implementation of gridless routing based on content addressable memory
DAC '90 Proceedings of the 27th ACM/IEEE Design Automation Conference
A negative reinforcement method for PGA routing
DAC '93 Proceedings of the 30th international Design Automation Conference
Shortest paths in the plane with polygonal obstacles
Journal of the ACM (JACM)
Shortest path queries among weighted obstacles in the rectilinear plane
Proceedings of the eleventh annual symposium on Computational geometry
The Smallest Pair of Noncrossing Paths in a Rectilinear Polygon
IEEE Transactions on Computers
DUNE: a multi-layer gridless routing system with wire planning
ISPD '00 Proceedings of the 2000 international symposium on Physical design
ISPD '00 Proceedings of the 2000 international symposium on Physical design
An implicit connection graph maze routing algorithm for ECO routing
ICCAD '99 Proceedings of the 1999 IEEE/ACM international conference on Computer-aided design
Single step current driven routing of multiterminal signal nets for analog applications
DATE '00 Proceedings of the conference on Design, automation and test in Europe
A minimum cost path search algorithm through tile obstacles
Proceedings of the 2001 international symposium on Physical design
Proceedings of the 2000 IEEE/ACM international conference on Computer-aided design
On Bends and Distances of Paths Among Obstacles in Two-Layer Interconnection Model
IEEE Transactions on Computers
Routing using implicit connection graphs [VLSI design
VLSID '96 Proceedings of the 9th International Conference on VLSI Design: VLSI in Mobile Communication
An efficient tile-based ECO router with routing graph reduction and enhanced global routing flow
Proceedings of the 2005 international symposium on Physical design
CDCTree: novel obstacle-avoiding routing tree construction based on current driven circuit model
ASP-DAC '06 Proceedings of the 2006 Asia and South Pacific Design Automation Conference
An-OARSMan: obstacle-avoiding routing tree construction with good length performance
Proceedings of the 2005 Asia and South Pacific Design Automation Conference
Proceedings of the 2006 international symposium on Physical design
A full-scale solution to the rectilinear obstacle-avoiding Steiner problem
Integration, the VLSI Journal
Obstacle-avoiding rectilinear Steiner tree construction
Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design
High-performance obstacle-avoiding rectilinear steiner tree construction
ACM Transactions on Design Automation of Electronic Systems (TODAES)
Generation of optimal obstacle-avoiding rectilinear Steiner minimum tree
Proceedings of the 2009 International Conference on Computer-Aided Design
Obstacle-avoiding rectilinear Steiner tree construction based on Steiner point selection
Proceedings of the 2009 International Conference on Computer-Aided Design
Approximation of octilinear steiner trees constrained by hard and soft obstacles
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
GD'09 Proceedings of the 17th international conference on Graph Drawing
Geographic knowledge discovery from Web Map segmentation through generalized Voronoi diagrams
Expert Systems with Applications: An International Journal
Computational Geometry: Theory and Applications
Rectilinear paths with minimum segment lengths
Discrete Applied Mathematics
Obstacle-avoiding rectilinear Steiner tree construction in sequential and parallel approach
Integration, the VLSI Journal
| Hi-index | 14.99 |
We study the rectilinear shortest paths and minimum spanning tree (MST) problems for a set of points in the plane in the presence of rectilinear obstacles. We use the track graph, a suitably defined grid-like structure, to obtain efficient solutions for both problems. The track graph consists of rectilinear tracks defined by the obstacles and the points for which shortest paths and a minimum spanning tree are sought. We use a growth process like Dijkstra's on the track graph to find shortest paths from any point in the set to all other points (the one-to-all shortest paths problem). For the one-to-all shortest paths problem for n points we derive an O(n min {log n, log e} + (e + k) log t) time algorithm, where e is the total number of edges of all obstacles, t is the number of extreme edges of all obstacles, and k is the number of intersections among obstacle tracks (all bounds are for the worst case). The MST for the points is constructed also in time O(n log n + (e + k) log t) by a hybrid method of searching for shortest paths while simultaneously constructing an MST. An interesting application of the MST algorithm is the approximation of Steiner trees in graphs.