Please note that eDoc will be permanently shut down in the first quarter of 2021!      Home News About Us Contact Contributors Disclaimer Privacy Policy Help FAQ

Home
Search
Quick Search
Advanced
Fulltext
Browse
Collections
Persons
My eDoc
Session History
Login
Name:
Password:
Documentation
Help
Support Wiki
Direct access to
document ID:


          Institute: MPI für Informatik     Collection: Algorithms and Complexity Group     Display Documents



ID: 517958.0, MPI für Informatik / Algorithms and Complexity Group
I/O-Efficient Dynamic Point Location in Monotone Subdivisions
Authors:Agarwal, Pankaj; Arge, Lars; Brodal, Gerth Stølting; Vitter, Jeffrey Scott
Language:English
Publisher:ACM
Place of Publication:New York, USA
Date of Publication (YYYY-MM-DD):1999
Title of Proceedings:Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA-99)
Start Page:11
End Page:20
Place of Conference/Meeting:Baltimore, USA
(Start) Date of Conference/Meeting
 (YYYY-MM-DD):
1999-01-17
End Date of Conference/Meeting 
 (YYYY-MM-DD):
1999-01-19
Audience:Experts Only
Intended Educational Use:No
Abstract / Description: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
$O(\log_{B}^{2} N)$ I/Os (worst-case) and updates in $O(\log_{B}^{2} N)$ I/Os
(amortized).

We also propose a new variant of $B$-trees, called
{\em level-balanced $B$-trees}, which allow insert, delete, merge,
and split operations in $O((1+\frac{b}{B}\log_{M/B} \frac{N}{B})\log_{b}
N)$ I/Os (amortized), $2\leq b\leq B/2$, even if each node stores a
pointer to its parent. Here $M$ is the size of main memory. Besides
being essential to our point-location data structure, we believe that
{\em level-balanced B-trees\/} are of significant independent
interest. They can, for example, be used to dynamically maintain a
planar st-graph using $O((1+\frac{b}{B}\log_{M/B} \frac{N}{B})\log_{b}
N)=O(\log_{B}^{2} N)$ I/Os (amortized) per update, so that reachability
queries can be answered in $O(\log_{B} N)$ I/Os (worst case).
Last Change of the Resource (YYYY-MM-DD):2010-03-02
External Publication Status:published
Document Type:Conference-Paper
Communicated by:Kurt Mehlhorn
Affiliations:MPI für Informatik/Algorithms and Complexity Group
Identifiers:LOCALID:C1256428004B93B8-AD0B65C4A88AB57EC1256702006673FF-...
ISBN:0-89871-434-6
The scope and number of records on eDoc is subject to the collection policies defined by each institute - see "info" button in the collection browse view.