An algorithm for planning collision-free paths among polyhedral obstacles
Communications of the ACM
On maximum flows in polyhedral domains
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Parallel rectilinear shortest paths with rectangular obstacles
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Shortest path queries in rectilinear worlds of higher dimension (extended abstract)
SCG '91 Proceedings of the seventh 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
Gross motion planning—a survey
ACM Computing Surveys (CSUR)
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
Rectilinear geodesics in 3-space (extended abstract)
Proceedings of the eleventh annual symposium on Computational geometry
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 sequential detailed router for huge grid graphs
Proceedings of the conference on Design, automation and test in Europe
Farthest neighbors and center points in the presence of rectngular obstacles
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Proceedings of the 39th annual Design Automation Conference
Touring a sequence of polygons
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Routing using implicit connection graphs [VLSI design
VLSID '96 Proceedings of the 9th International Conference on VLSI Design: VLSI in Mobile Communication
New results on shortest paths in three dimensions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
An efficient tile-based ECO router with routing graph reduction and enhanced global routing flow
Proceedings of the 2005 international symposium on Physical design
Efficient Rectilinear Steiner Tree Construction with Rectilinear Blockages
ICCD '05 Proceedings of the 2005 International Conference on Computer Design
Efficient obstacle-avoiding rectilinear steiner tree construction
Proceedings of the 2007 international symposium on Physical design
Finding rectilinear least cost paths in the presence of convex polygonal congested regions
Computers and Operations Research
Obstacle-avoiding rectilinear Steiner tree construction
Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design
Planar rectilinear shortest path computation using corridors
Computational Geometry: Theory and Applications
Generation of optimal obstacle-avoiding rectilinear Steiner minimum tree
Proceedings of the 2009 International Conference on Computer-Aided Design
Finding a rectilinear shortest path in R2using corridor based staircase structures
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
A nearly optimal algorithm for finding L1shortest paths among polygonal obstacles in the plane
ESA'11 Proceedings of the 19th European conference on Algorithms
Approximation of octilinear steiner trees constrained by hard and soft obstacles
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
An efficient algorithm for multi-layer obstacle-avoiding rectilinear Steiner tree construction
Proceedings of the 49th Annual Design Automation Conference
Computational Geometry: Theory and Applications
Rectilinear paths with minimum segment lengths
Discrete Applied Mathematics
A fast algorithm for rectilinear steiner trees with length restrictions on obstacles
Proceedings of the 2014 on International symposium on physical design
Obstacle-avoiding rectilinear Steiner tree construction in sequential and parallel approach
Integration, the VLSI Journal
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The problem of finding a rectilinear shortest path amongst obstacles may be stated as follows: Given a set of obstacles in the plane find a shortest rectilinear (L1) path from a point s to a point t which avoids all obstacles. The path may touch an obstacle but may not cross an obstacle. We study the rectilinear shortest path problem for the case where the obstacles are non-intersecting simple polygons, and present an &Ogr;(n (logn)2) algorithm for finding such a path, where n is the number of vertices of the obstacles. We also study the case of rectilinear obstacles in three dimensions, and show that L1 shortest paths can be found in &Ogr;(n2(log n)3) time.