Very sharp transitions in one-dimensional MANETs
- 1 January 2006
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- Vol. 1, 217-222
- https://doi.org/10.1109/icc.2006.254730
Abstract
We investigate how quickly phase transitions can occur in one-dimensional geometric random graph models of MANETs. In the case of graph connectivity and the absence of isolated nodes, we show that the transition width behaves like n-1 (when the number n of nodes is large), a significant improvement over asymptotic bounds given recently by Goel et al. for arbitrary monotone graph properties. We also outline how the approach used here could be applied in higher dimensions and for other graph properties.Keywords
This publication has 12 references indexed in Scilit:
- Threshold Functions, Node Isolation, and Emergent Lacunae in Sensor NetworksIEEE Transactions on Information Theory, 2006
- Monotone properties of random geometric graphs have sharp thresholdsThe Annals of Applied Probability, 2005
- Network connectivity of one-dimensional MANETs with random waypoint movementIEEE Communications Letters, 2005
- Order StatisticsWiley Series in Probability and Statistics, 2003
- The connectivity of a graph on uniform points on [0,1]dStatistics & Probability Letters, 2002
- On the connectivity in finite ad hoc networksIEEE Communications Letters, 2002
- The Probabilistic MethodPublished by Wiley ,2000
- Random GraphsPublished by Wiley ,2000
- A Strong Law for the Longest Edge of the Minimal Spanning TreeThe Annals of Probability, 1999
- The longest edge of the random minimal spanning treeThe Annals of Applied Probability, 1997