Improved Bounds for Wireless Localization

We consider a novel class of art gallery problems inspired by wireless localization that has recently been introduced by Eppstein, Goodrich, and Sitchinava. Given a simple polygon  P , place and orient guards each of which broadcasts a unique key within a fixed angular range. In contrast to the clas...

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Bibliographic Details
Published in:Algorithmica Vol. 57; no. 3; pp. 499 - 516
Main Authors: Christ, Tobias, Hoffmann, Michael, Okamoto, Yoshio, Uno, Takeaki
Format: Journal Article Conference Proceeding
Language:English
Published: New York Springer-Verlag 01.07.2010
Springer
Subjects:
Algorithm Analysis and Problem Complexity
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Computer Science
Computer science; control theory; systems
Computer systems and distributed systems. User interface
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Exact sciences and technology
Logical, boolean and switching functions
Mathematics of Computing
Software
Theoretical computing
Theory of Computation
Computational geometry
Art gallery problems
Lower bound
Upper bound
Boolean logic
Wireless network
Localization
Polygon
Art gallery
ISSN:0178-4617, 1432-0541
Online Access:Get full text
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Summary:We consider a novel class of art gallery problems inspired by wireless localization that has recently been introduced by Eppstein, Goodrich, and Sitchinava. Given a simple polygon  P , place and orient guards each of which broadcasts a unique key within a fixed angular range. In contrast to the classical art gallery setting, broadcasts are not blocked by the edges of  P . At any point in the plane one must be able to tell whether or not one is located inside P only by looking at the set of keys received. In other words, the interior of the polygon must be described by a monotone Boolean formula composed from the keys. We improve both upper and lower bounds for the general problem where guards may be placed anywhere by showing that the maximum number of guards to describe any simple polygon on n vertices is between roughly and . A guarding that uses at most guards can be obtained in O ( n log  n ) time. For the natural setting where guards may be placed aligned to one edge or two consecutive edges of  P only, we prove that n −2 guards are always sufficient and sometimes necessary.
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-009-9287-2