On the topologies of local minimum spanning trees

Authors:
P. F. Cortese;G. Di Battista;F. Frati;L. Grilli;K. A. Lehmann;G. Liotta;M. Patrignani;I. G. Tollis;F. Trotta
Affiliations:
Dipartimento di Informatica e Automazione, Università Roma Tre, Italy;Dipartimento di Informatica e Automazione, Università Roma Tre, Italy;Dipartimento di Informatica e Automazione, Università Roma Tre, Italy;Dipartimento di Ingegneria Elettronica e dell’Informazione, Università di Perugia, Italy;Wilhelm-Schickard Institut für Informatik, University of Tübingen, Germany;Dipartimento di Ingegneria Elettronica e dell’Informazione, Università di Perugia, Italy;Dipartimento di Informatica e Automazione, Università Roma Tre, Italy;Inst. of Computer Science, Foundation for Research and Technology Hellas-FORTH, Greece;Dipartimento di Ingegneria Elettronica e dell’Informazione, Università di Perugia, Italy
Venue:
CAAN'06 Proceedings of the Third international conference on Combinatorial and Algorithmic Aspects of Networking
Year:
2006

Citing 14
Cited 0

Transitions in geometric minimum spanning trees

Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Unit disk graph recognition is NP-hard

Computational Geometry: Theory and Applications - Special issue on geometric representations of graphs
A Survey of Energy Efficient Network Protocols for Wireless Networks

Wireless Networks
Routing with guaranteed delivery in ad hoc wireless networks

Wireless Networks
The drawability problem for minimum weight triangulations

Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
The Strength of Weak Proximity

GD '95 Proceedings of the Symposium on Graph Drawing
Worst-Case optimal and average-case efficient geometric ad-hoc routing

Proceedings of the 4th ACM international symposium on Mobile ad hoc networking & computing
On linear area embedding of planar graphs

On linear area embedding of planar graphs
Partial Delaunay Triangulation and Degree Limited Localized Bluetooth Scatternet Formation

IEEE Transactions on Parallel and Distributed Systems
On locally Delaunay geometric graphs

SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Unit disk graph approximation

Proceedings of the 2004 joint workshop on Foundations of mobile computing
A unified energy-efficient topology for unicast and broadcast

Proceedings of the 11th annual international conference on Mobile computing and networking
Localized Delaunay triangulation with application in ad hoc wireless networks

IEEE Transactions on Parallel and Distributed Systems

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper is devoted to study the combinatorial properties of Local Minimum Spanning Trees (LMSTs), a geometric structure that is attracting increasing research interest in the wireless sensor networks community. Namely, we study which topologies are allowed for a sensor network that uses, for supporting connectivity, a local minimum spanning tree approach. First, we refine the current definition of LMST realizability, focusing on the role of the power of transmission (i.e., of the radius of the covered area). Second, we show simple planar, connected, and triangle-free graphs with maximum degree 3 that cannot be represented as an LMST. Third, we present several families of graphs that can be represented as LMSTs. Then, we show a relationship between planar graphs and their representability as LMSTs based on homeomorphism. Finally, we show that the general problem of determining whether a graph is LMST representable is NP-hard.