Excluded minors, network decomposition, and multicommodity flow
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Randomized algorithms
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Mobility increases the capacity of ad hoc wireless networks
IEEE/ACM Transactions on Networking (TON)
Block Gossiping on Grids and Tori: Deterministic Sorting and Routing Match the Bisection Bound
ESA '93 Proceedings of the First Annual European Symposium on Algorithms
On the maximum stable throughput problem in random networks with directional antennas
Proceedings of the 4th ACM international symposium on Mobile ad hoc networking & computing
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
A New Min-Cut Max-Flow Ratio for Multicommodity Flows
SIAM Journal on Discrete Mathematics
Challenges: towards truly scalable ad hoc networks
Proceedings of the 13th annual ACM international conference on Mobile computing and networking
Capacity regions for wireless ad hoc networks
IEEE Transactions on Wireless Communications
The capacity of wireless networks
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
A deterministic approach to throughput scaling in wireless networks
IEEE Transactions on Information Theory
Stability and capacity of regular wireless networks
IEEE Transactions on Information Theory
Closing the Gap in the Capacity of Wireless Networks Via Percolation Theory
IEEE Transactions on Information Theory
Transmission Capacity of Wireless Ad Hoc Networks With Successive Interference Cancellation
IEEE Transactions on Information Theory
Hierarchical Cooperation Achieves Optimal Capacity Scaling in Ad Hoc Networks
IEEE Transactions on Information Theory
Product Multicommodity Flow in Wireless Networks
IEEE Transactions on Information Theory
A novel approach to power allocation in wireless ad hoc networks
Proceedings of the 5th ACM workshop on Performance monitoring and measurement of heterogeneous wireless and wired networks
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We establish a tight max-flow min-cut theorem for multi-commodity routing in random geometric graphs. We show that, as the number of nodes in the network n tends to infinity, the maximum concurrent flow (MCF) and the minimum cut-sparsity scale as Θ(n2r3(n)/k) for a random choice of k = Ω(n) source-destination pairs, where n and r(n) are the number of nodes and the communication range in the network respectively. The MCF equals the interference-free capacity of an ad-hoc network. We exploit this fact to develop novel graph theoretic techniques that can be used to deduce tight order bounds on the capacity of ad-hoc networks. We generalize all existing capacity results reported to date by showing that the per-commodity capacity of the network scales as Θ(1/r(n)k) for the single-packet reception model suggested by Gupta and Kumar, and as Θ(nr(n)/k) for the multiple-packet reception model suggested by others. More importantly, we show that, if the nodes in the network are capable of (perfect) multiple-packet transmission (MPT) and reception (MPR), then it is feasible to achieve the optimal scaling of Θn2r3(n)/k), despite the presence of interference. In comparison to the Gupta-Kumar model, the realization of MPT and MPR may require the deployment of a large number of antennas at each node or bandwidth expansion. Nevertheless, in stark contrast to the existing literature, our analysis presents the possibility of actually increasing the capacity of ad-hoc networks with n even while the communication range tends to zero!