Computational geometry: an introduction
Computational geometry: an introduction
Routing with guaranteed delivery in ad hoc wireless networks
DIALM '99 Proceedings of the 3rd international workshop on Discrete algorithms and methods for mobile computing and communications
On an improved algorithm for decentralized extrema finding in circular configurations of processors
Communications of the ACM
Decentralized extrema-finding in circular configurations of processors
Communications of the ACM
Geometric spanner for routing in mobile networks
MobiHoc '01 Proceedings of the 2nd ACM international symposium on Mobile ad hoc networking & computing
Distributed Algorithms
Location-based localized alternate, disjoint and multi-path routing algorithms for wireless networks
Journal of Parallel and Distributed Computing - Special issue on wireless and mobile ad hoc networking and computing
Design and Analysis of Distributed Algorithms (Wiley Series on Parallel and Distributed Computing)
Design and Analysis of Distributed Algorithms (Wiley Series on Parallel and Distributed Computing)
Local solutions for global problems in wireless networks
Journal of Discrete Algorithms
Approximate MST for UDG locally
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Local construction of planar spanners in unit disk graphs with irregular transmission ranges
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
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In a planar geometric network vertices are located in the plane, and edges are straight line segments connecting pairs of vertices, such that no two of them intersect. In this paper we study distributed computing in asynchronous, failure-free planar geometric networks, where each vertex is associated to a processor, and each edge to a bidirectional message communication link. Processors are aware of their locations in the plane. We consider fundamental computational geometry problems from the distributed computing point of view, such as finding the convex hull of a geometric network and identification of the external face. We also study the classic distributed computing problem of leader election, to understand the impact that geometric information has on the message complexity of solving it. We obtain an O(nlog^2n) message complexity algorithm to find the convex hull, and an O(nlogn) message complexity algorithm to identify the external face of a geometric network of n processors. We present a matching lower bound for the external face problem. We prove that the message complexity of leader election in a geometric ring is @W(nlogn), hence geometric information does not help in reducing the message complexity of this problem.