On Connecting Red and Blue Rectilinear Polygonal Obstacles with Nonintersecting Monotone Rectilinear Paths

We present efficient algorithms for the problems of matching red and blue disjoint geometric obstacles in the plane and connecting the matched obstacle pairs with mutually nonintersecting paths tha...

[1]  Chak-Kuen Wong,et al.  Rectilinear Path Problems among Rectilinear Obstacles Revisited , 1995, SIAM J. Comput..

[2]  D. T. Lee,et al.  Shortest rectilinear paths among weighted obstacles , 1990, SCG '90.

[3]  D. T. Lee,et al.  Rectilinear shortest paths in the presence of rectangular barriers , 1989, Discret. Comput. Geom..

[4]  Der-Tsai Lee,et al.  Shortest rectilinear paths among weighted rectangles , 1989 .

[5]  Michiel H. M. Smid,et al.  Lower bounds for computing geometric spanners and approximate shortest paths , 1996, Discret. Appl. Math..

[6]  Victor O. K. Li,et al.  Finding minimum rectilinear distance paths in the presence of barriers , 1981, Networks.

[7]  Franco P. Preparata,et al.  Testing a Simple Polygon for Monotonicity , 1981, Inf. Process. Lett..

[8]  Robert E. Tarjan,et al.  Finding Biconnected Components and Computing Tree Functions in Logarithmic Parallel Time (Extended Summary) , 1984, FOCS.

[9]  Joseph S. B. Mitchell,et al.  Shortest paths among obstacles in the plane , 1993, SCG '93.

[10]  Takao Nishizeki,et al.  Algorithms for Finding Non-Crossing Paths with Minimum Total Length in Plane Graphs , 1992, ISAAC.

[11]  Chak-Kuen Wong,et al.  Rectilinear Shortest Paths and Minimum Spanning Trees in the Presence of Rectilinear Obstacles , 1987, IEEE Transactions on Computers.

[12]  Danny Ziyi Chen,et al.  Shortest Path Queries Among Weighted Obstacles in the Rectilinear Plane , 2000, SIAM J. Comput..

[13]  Danny Ziyi Chen,et al.  Efficient Geometric Algorithms on the EREW PRAM , 1995, IEEE Trans. Parallel Distributed Syst..

[14]  Binay K. Bhattacharya,et al.  Efficient Approximate Shortest-Path Queries Among Isothetic Rectangular Obstacles , 1993, WADS.

[15]  Richard Cole,et al.  Cascading Divide-and-Conquer: A Technique for Designing Parallel Algorithms , 1987, FOCS.

[16]  Kenneth L. Clarkson,et al.  Rectilinear shortest paths through polygonal obstacles in O(n(logn)2) time , 1987, SCG '87.

[17]  Mikhail J. Atallah,et al.  On Parallel Rectilinear Obstacle- Avoiding Paths , 1993, Comput. Geom..

[18]  Tetsuo Asano,et al.  Routing Region Definition and Ordering Scheme for Building-Block Layout , 1985, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[19]  Danny Ziyi Chen,et al.  Rectilinear Short Path Queries Among Rectangular Obstacles , 1996, Inf. Process. Lett..

[20]  Neil L. White A nonuniform matroid which violates the isotopy conjecture , 1989, Discret. Comput. Geom..

[21]  Chwan-Chia Wu Time Redundant Fault-Location in Bit-Sliced ALU's , 1987, IEEE Transactions on Computers.

[22]  Mikhail J. Atallah,et al.  Parallel Rectilinear Shortest Paths with Rectangular Obstacles , 1991, Comput. Geom..

[23]  Andrew Chi-Chih Yao Lower bounds for algebraic computation trees with integer inputs , 1989, 30th Annual Symposium on Foundations of Computer Science.

[24]  Chee Yap,et al.  Rectilinear geodesics in 3-space , 1995 .

[25]  Takao Nishizeki,et al.  Finding Shortest Non-Crossing Rectilinear Paths in Plane Regions , 1993, ISAAC.

[26]  Mark de Berg,et al.  Shortest path queries in rectilinear worlds of higher dimension (extended abstract) , 1991, SCG '91.

[27]  Michael Ben-Or,et al.  Lower bounds for algebraic computation trees , 1983, STOC.

[28]  Jan van Leeuwen,et al.  Maintenance of Configurations in the Plane , 1981, J. Comput. Syst. Sci..

[29]  Evanthia Papadopoulou,et al.  k-Pairs Non-Crossing Shortest Paths in a Simple Polygon , 1996, Int. J. Comput. Geom. Appl..

[30]  Pinaki Mitra,et al.  Orthogonal shortest route queries among axis parallel rectangular obstacles , 1994, Int. J. Comput. Geom. Appl..

[31]  Chak-Kuen Wong,et al.  On Some Distance Problems in Fixed Orientations , 1987, SIAM J. Comput..

[32]  Mikhail J. Atallah A Matching Problem in the Plane , 1985, J. Comput. Syst. Sci..

[33]  Chak-Kuen Wong,et al.  On the X-Y convex hull of a set of X-Y polygons , 1983, BIT Comput. Sci. Sect..

[34]  Michael T. Goodrich,et al.  Finding the Convex Hull of a Sorted Point Set in Parallel , 1987, Inf. Process. Lett..

[35]  D. T. Lee,et al.  Parallel Algorithms for Maximum Matching in Complements of Interval Graphs and Related Problems , 2000, Algorithmica.