Discrete Mathematics - Topics on domination
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
GPSR: greedy perimeter stateless routing for wireless networks
MobiCom '00 Proceedings of the 6th annual international conference on Mobile computing and networking
Robust position-based routing in wireless Ad Hoc networks with unstable transmission ranges
DIALM '01 Proceedings of the 5th international workshop on Discrete algorithms and methods for mobile computing and communications
Geometric spanner for routing in mobile networks
MobiHoc '01 Proceedings of the 2nd ACM international symposium on Mobile ad hoc networking & computing
Wireless Communications: Principles and Practice
Wireless Communications: Principles and Practice
Distributed Maintenance of Resource Efficient Wireless Network Topologies (Distinguished Paper)
Euro-Par '02 Proceedings of the 8th International Euro-Par Conference on Parallel Processing
Ad-hoc networks beyond unit disk graphs
DIALM-POMC '03 Proceedings of the 2003 joint workshop on Foundations of mobile computing
Simple Robotic Routing in Ad Hoc Networks
ICNP '05 Proceedings of the 13TH IEEE International Conference on Network Protocols
Lazy cross-link removal for geographic routing
Proceedings of the 4th international conference on Embedded networked sensor systems
Geographic routing made practical
NSDI'05 Proceedings of the 2nd conference on Symposium on Networked Systems Design & Implementation - Volume 2
Planar graph routing on geographical clusters
Ad Hoc Networks
Energy-Efficient face routing on the virtual spanner
ADHOC-NOW'06 Proceedings of the 5th international conference on Ad-Hoc, Mobile, and Wireless Networks
A localized planarization algorithm for realistic wireless networks
WOWMOM '11 Proceedings of the 2011 IEEE International Symposium on a World of Wireless, Mobile and Multimedia Networks
Localized Delaunay triangulation with application in ad hoc wireless networks
IEEE Transactions on Parallel and Distributed Systems
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In wireless networks, the planar embedding of the communication network is often used in applications such as topology control and routing. Typically, wireless networks are nonplanar and hence algorithms which use local information are often applied to create planar graphs. These algorithms provably yield a connected planar graph as long as the network obeys certain assumptions like Unit Disk Graph (UDG). In this paper we propose a new explicit localized graph planarization algorithm to planarize graphs that are more general than UDGs, i.e. graphs satisfying redundancy property and a new property introduced by us called coexistence property. This algorithm detects intersections locally and planarizes networks by removing them. A link addition phase ensures that the network remains connected after the planarization algorithm. Theoretical analysis shows that our algorithm provably creates planar graphs without disconnecting the network graph if it has redundancy and coexistence properties. We also show these planar graphs are weak c-spanners at least in UDG modeled networks. Empirical analysis shows that they are as good as the best state of the art localized planarization algorithm with respect to the spanning ratio.