Leveraging Channel Diversity to Gain Efficiency and Robustness for Wireless Broadcast

Abstract

This paper addresses two primary questions: (i) How much faster can we disseminate information in a large wireless network if we have multiple communication channels available (as compared to relying on only a single communication channel)? (ii) Can we still disseminate information reliably, even if some subset of the channels are disrupted? In answer to the first question, we reduce the cost of broadcast to O(log log n) rounds/hop, approximately, for sufficiently many channels. We answer the second question in the affirmative, presenting two different algorithms, while at the same time proving a lower bound showing that disrupted channels have unavoidable costs.In more detail, we present upper and lower bounds for the multihop broadcast problem in the tdisrupted radio network model. This model assumes that in every round: each processes can participate on 1 out of C available communication channels, of which up to t < C might be locally disrupted, preventing communication. This model captures the unpredictable message loss that plagues real radio networks. We begin by studying the case with no disruption (t = 0) and present a randomized algorithm that solves broadcast in O((D + log n)(log C + log n C ) rounds, w.h.p., where D is the network diameter and n is the network size. Notice, for a single channel (C = 1), our algorithm has the same running time as the canonical Bar-Yehuda et al. algorithm [3], but as the number of channels increases so does our algorithm's performance advantage. We then prove that for a sufficiently large number of channels, our algorithm is within a O(log log n) factor of optimal.Having shown that multiple channels yield efficiency, we next turn our attention to showing that they also yield robustness. We now consider a setting with adversarial disruption (t > 0) and a common source of randomness. We present a randomized algorithm that solves broadcast in O((D + log n)( C log C log log C C−t + log n C−t )) rounds. For t up to a constant factor of C, this algorithm performs only a factor of O(log log C) slower than the no disruption case: that is, even with significant disruption, our multi-channel algorithm still outperforms solutions that assume a single, perfectly reliable channel. For completeness, we conclude by considering the case with disruption and no common randomness. We demonstrate a clear separation with the common randomness case by proving a lower bound of Ω((D +log n) Ct C−t ) rounds, and then presenting an almost matching randomized upper bound that solves broadcast in O((D + log n) Ct C−t log ( n t )) rounds, w.h.p.

Maximal independent sets in multichannel radio networks

“…These bounds (nearly) match the relevant Ω D + log 2 n F bound for multichannel networks [16], and beat the relevant Ω(D + log 2 n) lower bound for single channel networks [3]. Related Work.…”

“…For F = log n, this yields results similar to this paper, i.e., O(D) +Õ(log n). The results are hard to compare, however, as [16] assumes collision detection (which we do not), but we assume bounded independence (which [16] does not).…”

“…These techniques did not directly translate to multihop networks. We also have studied the problem of broadcast in multihop networks [16]. In this case, we assumed that nodes had access to collision detection, showing how to leverage this information to solve broadcast in O D + log n log F + log n F .…”

Frequency Hopping against a Powerful Adversary

“…Dolev et al [9] studied jamming in the context of multi-channel gossip and presented tight bounds for the -gossip problem, where the adversary may jam 1 frequency per round. They also study a setting allowing the nodes to exchange authenticated messages despite a malicious adversary that can cause collisions and spoof messages [10], and present new bounds on broadcasting [11]. Another line of work focuses on the bootstrap problem where nodes have to find each other despite adversarial jammers [23,8,4].…”

Leveraging multiple channels in ad hoc networks

“…Diversity in wireless networks -having multiple opportunities for communication -is well known to decrease interference, increase reliability, and improve performance [5,9]. The question is how much it helps and what the limits are to such improvements.…”