A nearly best-possible approximation algorithm for node-weighted Steiner trees
Journal of Algorithms
On k-connectivity for a geometric random graph
Random Structures & Algorithms
Journal of Algorithms
Improved Steiner tree approximation in graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
On the minimum node degree and connectivity of a wireless multihop network
Proceedings of the 3rd ACM international symposium on Mobile ad hoc networking & computing
Guarding Galleries and Terrains
TCS '02 Proceedings of the IFIP 17th World Computer Congress - TC1 Stream / 2nd IFIP International Conference on Theoretical Computer Science: Foundations of Information Technology in the Era of Networking and Mobile Computing
Using Bounded Degree Spanning Trees in the Design of Efficient Algorihtms on Claw-Free Graphs
WADS '89 Proceedings of the Workshop on Algorithms and Data Structures
Sharp thresholds For monotone properties in random geometric graphs
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
The capacity of wireless networks
IEEE Transactions on Information Theory
A survey on position-based routing in mobile ad hoc networks
IEEE Network: The Magazine of Global Internetworking
Combinatorics, Probability and Computing
Combinatorics, Probability and Computing
Modeling and connectivity analysis in obstructed wireless ad hoc networks
Proceedings of the 15th ACM international conference on Modeling, analysis and simulation of wireless and mobile systems
Communication problems in random line-of-sight ad-hoc radio networks
SAGA'07 Proceedings of the 4th international conference on Stochastic Algorithms: foundations and applications
Connectivity in obstructed wireless networks: from geometry to percolation
Proceedings of the fourteenth ACM international symposium on Mobile ad hoc networking and computing
| Hi-index | 0.00 |
Random geometric graphs have been one of the fundamental models for reasoning about wireless networks: one places n points at random in a region of the plane (typically a square or circle), and then connects pairs of points by an edge if they are within a fixed distance of one another. In addition to giving rise to a range of basic theoretical questions, this class of random graphs has been a central analytical tool in the wireless networking community. For many of the primary applications of wireless networks, however, the underlying environment has a large number of obstacles, and communication can only take place among nodes when they are close in space and when they have line-of-sight access to one another --- consider, for example, urban settings or large indoor environments. In such domains, the standard model of random geometric graphs is not a good approximation of the true constraints, since it is not designed to capture the line-of-sight restrictions. Here we propose a random-graph model incorporating both range limitations and line-of-sight constraints, and we prove asymptotically tight results for κ-connectivity. Specifically, we consider points placed randomly on a grid (or torus), such that each node can see up to a fixed distance along the row and column it belongs to. (We think of the rows and columns as "streets" and "avenues" among a regularly spaced array of obstructions.) Further, we show that when the probability of node placement is a constant factor larger than the threshold for connectivity, near-shortest paths between pairs of nodes can be found, with high probability, by an algorithm using only local information. In addition to analyzing connectivity and κ-connectivity, we also study the emergence of a giant component, as well an approximation question, in which we seek to connect a set of given nodes in such an environment by adding a small set of additional "relay" nodes.