1,383 research outputs found
Parallel Transitive Closure and Point Location in Planar Structures
AMS(MOS) subject classifications. 68E05, 68C05, 68C25Parallel algorithms for several graph and geometric problems are presented, including transitive closure and topological sorting in planar st-graphs, preprocessing planar subdivisions for point location queries, and construction of visibility representations and drawings of planar graphs.
Most of these algorithms achieve optimal O(logn) running time using n/logn processors in the EREW PRAM model, n being the number of vertices
I/O-efficient dynamic point location in monotone planar subdivisions
We present an efficient external-memory dynamic data structure for point location in monotone planar subdivisions. Our data structure uses O(N/B) disk blocks to store a monotone subdivision of size N, where B is the size of a disk block. It supports queries in O(logi N) I/OS (worst-case) and updates
in O(lo& N) I/OS (amortized). We also propose a new variant of B-trees, called leuelbalanced
B-trees, which allow insert, delete, merge, and split
operations in O((l+ 10g~,~ ) log, N) = O(logi N) I/OS (amortized) per update, so that reachability queries can be answered in O(log, N) I/OS (worst case)
A Report On Planar Point Location: Some New Techniques
Report on point location query on a planar straight line graph measuring processing time, space complexity, and query time
Dynamic Planar Point Location in External Memory
In this paper we describe a fully-dynamic data structure for the planar point location problem in the external memory model. Our data structure supports queries in O(log_B n(log log_B n)^3)) I/Os and updates in O(log_B n(log log_B n)^2)) amortized I/Os, where n is the number of segments in the subdivision and B is the block size. This is the first dynamic data structure with almost-optimal query cost. For comparison all previously known results for this problem require O(log_B^2 n) I/Os to answer queries. Our result almost matches the best known upper bound in the internal-memory model
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