Dynamic planar point location with optimal query time

1989 ◽  
pp. 84-95 ◽  
Author(s):  
Franco P. Preparata ◽  
Roberto Tamassia
Keyword(s):  
Query Time ◽  
Point Location ◽  
Planar Point ◽  
Planar Point Location

scholarly journals Dynamic planar point location with optimal query time

1990 ◽  
Vol 74 (1) ◽  
pp. 95-114 ◽  
Author(s):  
Franco P. Preparata ◽  
Roberto Tamassia
Keyword(s):  
Query Time ◽  
Point Location ◽  
Planar Point ◽  
Planar Point Location

scholarly journals Lower Bounds for Dynamic Transitive Closure, Planar Point Location, and Parentheses Matching

1996 ◽  
Vol 3 (9) ◽  
Author(s):  
Thore Husfeldt ◽  
Theis Rauhe ◽  
Søren Skyum
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Transitive Closure ◽  
Unit Cost ◽  
Random Access ◽  
Point Location ◽  
Worst Case ◽  
Planar Point ◽  
Planar Point Location ◽  
Prefix Sums

We give a number of new lower bounds in the cell probe model<br />with logarithmic cell size, which entails the same bounds on the random access computer with logarithmic word size and unit cost operations. We study the signed prefix sum problem: given a string of length n of zeroes and signed ones, compute the sum of its ith prefix during updates. We show a<br />lower bound of  Omega(log n/log log n) time per operations, even if the prefix sums are bounded by log n/log log n during all updates. We also show that if the update time is bounded by the product of the worst-case update time and the<br />answer to the query, then the update time must be Omega(sqrt(log n/ log log n)).<br /> These results allow us to prove lower bounds for a variety of seemingly unrelated<br />dynamic problems. We give a lower bound for the dynamic planar point location in monotone subdivisions of <br />Omega(log n/ log log n) per operation. We give<br />a lower bound for the dynamic transitive closure problem on upward planar graphs with one source and one sink of <br />Omega(log n/(log logn)^2) per operation. We give a lower bound of  Omega(sqrt(log n/log log n)) for the dynamic membership problem of any Dyck language with two or more letters. This implies the same<br />lower bound for the dynamic word problem for the free group with k generators. We also give lower bounds for the dynamic prefix majority and prefix equality problems.

Adaptive Planar Point Location

2021 ◽  
Vol 50 (4) ◽  
pp. 1200-1247
Author(s):  
Siu-Wing Cheng ◽  
Man-Kit Lau
Keyword(s):  
Point Location ◽  
Planar Point ◽  
Planar Point Location

scholarly journals Towards an Optimal Method for Dynamic Planar Point Location

2018 ◽  
Vol 47 (6) ◽  
pp. 2337-2361
Author(s):  
Timothy M. Chan ◽  
Yakov Nekrich
Keyword(s):  
Point Location ◽  
Optimal Method ◽  
Planar Point ◽  
Planar Point Location

scholarly journals AN IMPROVED HYPERCUBE BOUND FOR MULTISEARCHING AND ITS APPLICATIONS

1999 ◽  
Vol 09 (01) ◽  
pp. 29-38
Author(s):  
MIKHAIL J. ATALLAH
Keyword(s):  
Data Structure ◽  
Constant Time ◽  
Search Problem ◽  
Parallel Search ◽  
Point Location ◽  
Planar Point ◽  
Geometric Problems ◽  
Trapezoidal Decomposition ◽  
Planar Point Location ◽  
Hypercube Model

We give a result that implies an improvement by a factor of log log  n in the hypercube bounds for the geometric problems of batched planar point location, trapezoidal decomposition, and polygon triangulation. The improvements are achieved through a better solution to the multisearch problem on a hypercube, a parallel search problem where the elements in the data structure S to be searched are totally ordered, but where it is not possible to compare in constant time any two given queries q and q′. Whereas the previous best solution to this problem took O( log  n( log log  n)3) time on an n-processor hypercube, the solution given here takes O( log  n( log log  n)2) time on an n-processor hypercube. The hypercube model for which we claim our bounds is the standard one, SIMD, with O(1) memory registers per processor, and with one-port communication. Each register can store O( log  n) bits, so that a processor knows its ID.

scholarly journals Planar Point Location Using Persistent Search Trees

1989 ◽  
Vol 555 (1 Combinatorial) ◽  
pp. 352-362
Author(s):  
NEIL SARNAK ◽  
ROBERT E. TARJAN
Keyword(s):  
Search Trees ◽  
Point Location ◽  
Planar Point ◽  
Planar Point Location
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