With the availability of multiple unlicensed spectral bands, and potential cost-based limitations on the capabilities of individual nodes, it is increasingly relevant to study the performance of multichannel wireless networks with channel switching constraints. To this effect, some constraint models have been recently proposed, and connectivity and capacity results have been formulated for networks of randomly deployed single-interface nodes subject to these constraints. One of these constraint models is termed random (c, f) assignment, wherein each node is pre-assigned a random subset of f channels out of c (each having bandwidth W c), and may only switch on these. Previous results for this model established bounds on network capacity, and proved that when c = O(logn), the per-prnd f flow capacity is O(W nlogn) and Ω(W cnlogn) (where prnd = 1 −(1 − f f f f 2 c)(1 − c−1)...(1 − c − f+1) ≥ 1 − e − c). In this paper we present a lower bound construction that matches the previous upper prnd bound. This establishes the capacity as Θ(W nlogn). The surprising implication of this result is that when f = Ω ( √ c), random (c, f) assignment yields capacity of the same order as attainable via unconstrained switching. The routing/scheduling procedure used by us to achieve capacity requires synchronized route-construction for all flows in the network, leading to the open question of whether it is possible to achieve capacity using asynchronous procedures.

We study oblivious deterministic gossip algorithms for multi-channel radio networks with a malicious adversary. In a multi-channel network, each of the n processes in the system must choose, in each round, one of the c channels of the system on which to participate. Assuming the adversary can disrupt one channel per round, “preventing“ communication on that channel, we establish (1−ɛ)n a tight bound of max Θ c−1 + logc n n(1−ɛ), Θ ɛc2 ”” on the number of rounds needed to solve the ɛ-gossip problem, a parameterized generalization of the all-to-all gossip problem that requires (1 − ɛ)n of the “rumors ” to be successfully disseminated. Underlying our lower bound proof lies an interesting connection between ɛ-gossip and extremal graph theory. Specifically, we make use of Turán’s theorem, a seminal result in extremal combinatorics, to reason about an adversary’s optimal strategy for disrupting an algorithm of a given duration. We then show how to generalize our upper bound to cope with an adversary that can simultaneously disrupt t < c channels. Our generalization makes use of selectors: a combinatorial tool that guarantees that any subset of processes will be “selected ” by some set in the selector. We prove this generalized algorithm optimal if a maximum number of values is to be gossiped. We conclude by extending our algorithm to tolerate traditional Byzantine corruption faults.

Recent years have seen significant interest in using the multihop wireless networking paradigm for building mesh networks, ad hoc networks, and sensor networks. A key challenge in multihop wireless networks is to provision for sufficient network capacity to meet user requirements. Several approaches have been proposed to improve the network capacity in multihop networks, ranging from approaches that improve the efficiency of existing protocols, to approaches that use additional resources. In this dissertation, we propose to use additional frequency spectrum, as well as improve the efficiency of using existing frequency spectrum, for improving network capacity. Widely used wireless technologies, such as IEEE 802.11, provision for multiple frequencyseparated channels in the available frequency spectrum. Commercially available wireless network interfaces can typically operate over only one channel at a time. Due to cost and complexity constraints, the total number of interfaces at each node is expected to be fewer than the total number of channels available in the network. Under this scenario with fewer interfaces per node than channels, several challenges have to be addressed before all the channels can be utilized. In this dissertation, we have established the asymptotic capacity of multichannel wireless networks with varying number of channels and interfaces. Capacity analysis has shown that it is feasible

Abstract — It is usual to quantify the performance of communication networks in terms of achievable throughput or delay. However, as a result of the significant recent interest in safety-critical application scenarios for wireless networking, security and reliability concerns are gradually emerging at the forefront of wireless networking research. In light of this, it is increasingly crucial to consider secure communication capacity or delay as primary performance measures, and evolve theoretical frameworks that can allow for quantification of the trade-off between security and performance. In this paper, we argue for the need for comprehensive effort in this direction, and present an illustrative example of the same by describing asymptotic secure-capacity results for randomly deployed wireless network where each node is preloaded with a random subset of keys. I.