Randomized algorithms
Tail bounds for occupancy and the satisfiability threshold conjecture
Random Structures & Algorithms
Simple proofs of occupancy tail bounds
Random Structures & Algorithms
The Power of Two Choices in Randomized Load Balancing
IEEE Transactions on Parallel and Distributed Systems
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Semidefinite programming for ad hoc wireless sensor network localization
Proceedings of the 3rd international symposium on Information processing in sensor networks
Proceedings of the 5th ACM international symposium on Mobile ad hoc networking and computing
Theory of semidefinite programming for sensor network localization
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Capacity of multi-channel wireless networks: impact of number of channels and interfaces
Proceedings of the 11th annual international conference on Mobile computing and networking
Distributed localization using noisy distance and angle information
Proceedings of the 7th ACM international symposium on Mobile ad hoc networking and computing
On the θ-coverage and connectivity of large random networks
IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
Coverage by randomly deployed wireless sensor networks
IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
Localization in sparse networks using sweeps
Proceedings of the 12th annual international conference on Mobile computing and networking
Multicast capacity for large scale wireless ad hoc networks
Proceedings of the 13th annual ACM international conference on Mobile computing and networking
The multicast capacity of large multihop wireless networks
Proceedings of the 8th ACM international symposium on Mobile ad hoc networking and computing
The capacity of wireless networks
IEEE Transactions on Information Theory
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The traditional coupon collector's problem studies the number of balls required to fill n bins if the balls are placed into bins uniformly at random. It is folklore that ***(n ln n ) balls are required to fill the bins with high probability (w.h.p. ). In this paper, we study a variation of the random ball placement process. In each round, we assume the ability to acquire the set of empty bins after previous rounds and exclusively place balls into them uniformly at random. For such a k -round random ball placement process (k -RBP), we derive a sharp threshold of n ln [k ] n balls for filling n bins. We apply the bounds of k -RBP to the wireless sensor network deployment problem. Assume the communication range for the sensors is r and the deployment region is a 2D unit square. Let n = (1/r )2. We show that the number of random nodes needed to achieve connectivity is ***(n ln ln n ) if we are given a "second chance" to deploy nodes, improving the previous ***(n ln n ) bounds [8] in the one round case. More generally, under certain deployment assumption, if the random deployment in i -th round can utilize the information from the previous i *** 1 rounds, the asymptotic number of nodes to satisfy connectivity is ***(n ln [k ] n ) for k rounds. Similar results also hold if the sensing regions of the deployed nodes are required to cover the region of interest.