Discrete Mathematics - Topics on domination
Smallest-last ordering and clustering and graph coloring algorithms
Journal of the ACM (JACM)
On k-connectivity for a geometric random graph
Random Structures & Algorithms
Random channel assignment in the plane
Random Structures & Algorithms
Proceedings of the 5th ACM international symposium on Mobile ad hoc networking and computing
On deriving the upper bound of α-lifetime for large sensor networks
Proceedings of the 5th ACM international symposium on Mobile ad hoc networking and computing
Coverage by randomly deployed wireless sensor networks
IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
IEEE Transactions on Parallel and Distributed Systems
| Hi-index | 5.23 |
In wireless networks, to avoid collisions of simultaneous transmissions over the same channel, adjacent nodes are assigned distinct channels, and the least number of channels used in an assignment is called the chromatic number. The determination of the chromatic number is NP-hard. In this paper, we introduce an analytic tool called maximum scan statistics. For a finite point set V and a convex compact set C, the maximum scan statistic of V with respect to the scanning set C is the largest number of points in V covered by a copy C. Based on the study of asymptotic maximum scan statistics, we obtain the asymptotics of the maximum degree and the clique number of homogeneous wireless networks. The results imply that the chromatic number is almost surely at most four times the clique number. We further prove that the approximation ratios of some vertex-ordering-based First-Fit channel assignment algorithms are almost surely bounded by 2. In the analysis, we also learn that the chromatic number is almost surely at most twice the clique number.