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Devices in a cognitive radio network use advanced radios to identify pockets of usable spectrum in a crowded band and make them available to higher layers of the network stack. A core challenge in designing algorithms for this model is that different devices might have different views of the network. In this paper, we study two problems for this setting that are well-motivated but not yet wellunderstood: local broadcast and data aggregation.We consider a single hop cognitive radio network with n nodes that each has access to c channels. We assume each pair of nodes overlaps on at least 1 ≤ k ≤ c channels.We first describe and analyze COGCAST, a randomized algorithm that solves local broadcast in O((c/k) · max{1, c/n} · lg n) time, with high probability, by spreading information in an epidemic manner through the network.We then propose COGCOMP, a randomized algorithm that solves data aggregation in O((c/k) · max{1, c/n} · lg n + n) time, with high probability. The COGCOMP algorithm uses COGCAST as a key primitive to establish a spanning tree among the nodes, so that data can be aggregated from leaves to root.We conclude with a collection of lower bounds that show COG-CAST is near optimal (in particular, within a lg n factor) in many cases. These bounds introduce new techniques of potential standalone interest for those concerned with proving fundamental limits in the cognitive radio network setting.

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In this paper, we consider contention resolution on a multiple-access communication channel. In this problem, a set of nodes arrive over time, each with a message it intends to send. In each time slot, each node may attempt to broadcast its message or remain idle. If a single node broadcasts in a slot, the message is received by all nodes; otherwise, if multiple nodes broadcast simultaneously, a collision occurs and none succeeds. If collision detection is available, nodes can differentiate collision and silence (i.e., no node broadcasts). Performance of contention resolution algorithms is often measured by throughput-the number of successful transmissions within a period of time; whereas robustness is often measured by jamming resistance-a jammed slot always generates a collision. Previous work has shown, with collision detection, optimal constant throughput can be attained, even if a constant fraction of all slots are jammed. The situation when collision detection is not available, however, remains unclear.In a recent breakthrough paper [Bender et al., STOC '20], a crucial case is resolved: constant throughput is possible without collision detection, but only if there is no jamming. Nonetheless, the exact trade-off between the best possible throughput and the severity of jamming remains unknown. In this paper, we address this open question. Specifically, for any level of jamming ranging from none to constant fraction, we prove an upper bound on the best possible throughput, along with an algorithm attaining that bound. An immediate and interesting implication of our result is, when a constant fraction of all slots are jammed, which is the asymptotic worst-case scenario, there still exists an algorithm achieving a decent throughput: Θ( /log ) messages could be successfully transmitted within slots.

Cognitive radio networks are a new type of multi-channel wireless network in which different nodes can have access to different sets of channels. By providing multiple channels, they improve the efficiency and reliability of wireless communication. However, the heterogeneous nature of cognitive radio networks also brings new challenges to the design and analysis of distributed algorithms.In this paper, we focus on two fundamental problems in cognitive radio networks: neighbor discovery, and global broadcast. We consider a network containing n nodes, each of which has access to c channels. We assume the network has diameter D, and each pair of neighbors have at least k ≥ 1, and at most k max ≤ c, shared channels. We also assume each node has at most ∆ neighbors. For the neighbor discovery problem, we design a randomized algorithm CSEEK which has time complexityÕ((c 2 /k) + (k max /k) · ∆). CSEEK is flexible and robust, which allows us to use it as a generic "filter" to find "well-connected" neighbors with an even shorter running time. We then move on to the global broadcast problem, and propose CGCAST, a randomized algorithm which takesCGCAST uses CSEEK to achieve communication among neighbors, and uses edge coloring to establish an efficient schedule for fast message dissemination.Towards the end of the paper, we give lower bounds for solving the two problems. These lower bounds demonstrate that in many situations, CSEEK and CGCAST are near optimal.