The abstract MAC layer

A diversity of possible communication assumptions complicates the study of algorithms and lower bounds for radio networks. We address this problem by defining an Abstract MAC Layer. This service provides reliable local broadcast communication, with timing guarantees stated in terms of a collection of abstract delay functions applied to the relevant contention. Algorithm designers can analyze their algorithms in terms of these functions, independently of specific channel behavior. Concrete implementations of the Abstract MAC Layer over basic radio network models generate concrete definitions for these delay functions, automatically adapting bounds proven for the abstract service to bounds for the specific radio network under consideration. To illustrate this approach, we use the Abstract MAC Layer to study the new problem of Multi-Message Broadcast, a generalization of standard single-message broadcast, in which any number of messages arrive at any processes at any times. We present and analyze two algorithms for Multi-Message Broadcast in static networks: a simple greedy algorithm and one that uses regional leaders. We then indicate how these results can be extended to mobile networks.Cisco Systems, Inc.Lehman Brothers (1993-2008)CUNY (A New MAC-Layer Paradigm for Mobile Ad-Hoc Networks)National Science Foundation (U.S.) (NSF Award Number CCF-0726514)National Science Foundation (U.S.) (NSF Award Number CNS-0715397

Byzantine Consensus in Abstract MAC Layer

This paper studies the design of Byzantine consensus algorithms in an asynchronous single-hop network equipped with the “abstract MAC layer” [DISC09], which captures core properties of modern wireless MAC protocols. Newport [PODC14], Newport and Robinson [DISC18], and Tseng and Zhang [PODC22] study crash-tolerant consensus in the model. In our setting, a Byzantine faulty node may behave arbitrarily, but it cannot break the guarantees provided by the underlying abstract MAC layer. To our knowledge, we are the first to study Byzantine faults in this model. We harness the power of the abstract MAC layer to develop a Byzantine approximate consensus algorithm and a Byzantine randomized binary consensus algorithm. Both of our algorithms require only the knowledge of the upper bound on the number of faulty nodes f, and do not require the knowledge of the number of nodes n. This demonstrates the “power” of the abstract MAC layer, as consensus algorithms in traditional message-passing models require the knowledge of both n and f. Additionally, we show that it is necessary to know f in order to reach consensus. Hence, from this perspective, our algorithms require the minimal knowledge. The lack of knowledge of n brings the challenge of identifying a quorum explicitly, which is a common technique in traditional message-passing algorithms. A key technical novelty of our algorithms is to identify “implicit quorums” which have the necessary information for reaching consensus. The quorums are implicit because nodes do not know the identity of the quorums – such notion is only used in the analysis

Fault-Tolerant Consensus with an Abstract MAC Layer

In this paper, we study fault-tolerant distributed consensus in wireless systems. In more detail, we produce two new randomized algorithms that solve this problem in the abstract MAC layer model, which captures the basic interface and communication guarantees provided by most wireless MAC layers. Our algorithms work for any number of failures, require no advance knowledge of the network participants or network size, and guarantee termination with high probability after a number of broadcasts that are polynomial in the network size. Our first algorithm satisfies the standard agreement property, while our second trades a faster termination guarantee in exchange for a looser agreement property in which most nodes agree on the same value. These are the first known fault-tolerant consensus algorithms for this model. In addition to our main upper bound results, we explore the gap between the abstract MAC layer and the standard asynchronous message passing model by proving fault-tolerant consensus is impossible in the latter in the absence of information regarding the network participants, even if we assume no faults, allow randomized solutions, and provide the algorithm a constant-factor approximation of the network size

Robust Leader Election in a Fast-Changing World

We consider the problem of electing a leader among nodes in a highly dynamic network where the adversary has unbounded capacity to insert and remove nodes (including the leader) from the network and change connectivity at will. We present a randomized Las Vegas algorithm that (re)elects a leader in O(D\log n) rounds with high probability, where D is a bound on the dynamic diameter of the network and n is the maximum number of nodes in the network at any point in time. We assume a model of broadcast-based communication where a node can send only 1 message of O(\log n) bits per round and is not aware of the receivers in advance. Thus, our results also apply to mobile wireless ad-hoc networks, improving over the optimal (for deterministic algorithms) O(Dn) solution presented at FOMC 2011. We show that our algorithm is optimal by proving that any randomized Las Vegas algorithm takes at least omega(D\log n) rounds to elect a leader with high probability, which shows that our algorithm yields the best possible (up to constants) termination time.Comment: In Proceedings FOMC 2013, arXiv:1310.459

Multi-message broadcast with abstract MAC layers and unreliable links

We study the multi-message broadcast problem using abstract MAC layer models of wireless networks. These models capture the key guarantees of existing MAC layers while abstracting away low-level details such as signal propagation and contention.We begin by studying upper and lower bounds for this problem in a standard abstract MAC layer model---identifying an interesting dependence between the structure of unreliable links and achievable time complexity. In more detail, given a restriction that devices connected directly by an unreliable link are not too far from each other in the reliable link topology, we can (almost) match the efficiency of the reliable case. For the related restriction, however, that two devices connected by an unreliable link are not too far from each other in geographic distance, we prove a new lower bound that shows that this efficiency is impossible. We then investigate how much extra power must be added to the model to enable a new order of magnitude of efficiency. In more detail, we consider an enhanced abstract MAC layer model and present a new multi-message broadcast algorithm that (under certain natural assumptions) solves the problem in this model faster than any known solutions in an abstract MAC layer setting.United States. Air Force Office of Scientific Research (FA9550-13-1-0042)Ford Motor Company. University Research ProgramNational Science Foundation (U.S.) (Grant CCF-1320279)National Science Foundation (U.S.) (Grant CCF-0939370)National Science Foundation (U.S.) (Grant CCF-1217506)National Science Foundation (U.S.) (Grant CCF-AF-0937274)MIT Center for Wireless Networks and Mobile Computin

Decomposing Broadcast Algorithms Using Abstract MAC Layers

In much of the theoretical literature on global broadcast algorithms for wireless networks, issues of message dissemination are considered together with issues of contention management. This combination leads to complicated algorithms and analysis, and makes it difficult to extend the work to more difficult communication problems. In this paper, we present results aimed at simplifying such algorithms and analysis by decomposing the treatment into two levels, using abstract "MAC layer" specifications to encapsulate contention management. We use two different abstract MAC layers: the basic layer of Kuhn, Lynch, and Newport, and a new probabilistic layer. We first present a typical randomized contention-management algorithm for a standard graph-based radio network model and show that it implements both abstract MAC layers. Then we combine this algorithm with greedy algorithms for single-message and multi-message global broadcast and analyze the combinations, using both abstract MAC layers as intermediate layers. Using the basic MAC layer, we prove a bound of O(D log(n / epsilon) log(Delta)) for the time to deliver a single message everywhere with probability 1 - epsilon, where D is the network diameter, n is the number of nodes, and Delta is the maximum node degree. Using the probabilistic layer, we prove a bound of O((D + log(n/epsilon)) log(Delta)), which matches the best previously-known bound for single-message broadcast over the physical network model. For multi-message broadcast, we obtain bounds of O((D + k Delta) log(n/epsilon) log(Delta)) using the basic layer and O((D + k Delta log(n/epsilon)) log(Delta)) using the probabilistic layer, for the time to deliver a message everywhere in the presence of at most k concurrent messages.Author Lynch's research is supported by AFOSR contract FA9550-08-1-0159 and NSF grants CCF-0726514, CNS-0715397, CCF-0937274, and NSF-PURDUE-STC Award 0939370-CCF. Author Kowalski's research is supported by the Engineering and Physical Sciences Research Council [grant numbers EP/G023018/1, EP/H018816/1]

A (Truly) Local Broadcast Layer for Unreliable Radio Networks

In this paper, we implement an efficient local broadcast service for the dual graph model, which describes communication in a radio network with both reliable and unreliable links. Our local broadcast service offers probabilistic latency guarantees for: (1) message delivery to all reliable neighbors (i.e., neighbors connected by reliable links), and (2) receiving some message when one or more reliable neighbors are broadcasting. This service significantly simplifies the design and analysis of algorithms for the otherwise challenging dual graph model. To this end, we also note that our solution can be interpreted as an implementation of the abstract MAC layer specification---therefore translating the growing corpus of algorithmic results studied on top of this layer to the dual graph model. At the core of our service is a seed agreement routine which enables nodes in the network to achieve "good enough" coordination to overcome the difficulties of unpredictable link behavior. Because this routine has potential application to other problems in this setting, we capture it with a formal specification---simplifying its reuse in other algorithms. Finally, we note that in a break from much work on distributed radio network algorithms, our problem definitions (including error bounds), implementation, and analysis do not depend on global network parameters such as the network size, a goal which required new analysis techniques. We argue that breaking the dependence of these algorithms on global parameters makes more sense and aligns better with the rise of ubiquitous computing, where devices will be increasingly working locally in an otherwise massive network. Our push for locality, in other words, is a contribution independent of the specific radio network model and problem studied here

Bounds on Contention Management in Radio Networks

The local broadcast problem assumes that processes in a wireless network are provided messages, one by one, that must be delivered to their neighbors. In this paper, we prove tight bounds for this problem in two well-studied wireless network models: the classical model, in which links are reliable and collisions consistent, and the more recent dual graph model, which introduces unreliable edges. Our results prove that the Decay strategy, commonly used for local broadcast in the classical setting, is optimal. They also establish a separation between the two models, proving that the dual graph setting is strictly harder than the classical setting, with respect to this primitive

The Cost of Global Broadcast Using Abstract MAC Layers

We analyze greedy algorithms for broadcasting messages throughout a multi-hop wireless network, using a slot-based model that includes message collisions without collision detection. Our algorithms are split formally into two pieces: a high-level piece for broadcast and a low-level piece for contention management. We accomplish the split using abstract versions of the MAC layer to encapsulate the contention management. We use two different abstract MAC layers: a basic non-probabilistic one, which our contention management algorithm implements with high probability, and a probabilistic one, which our contention management algorithm implements precisely. Using this approach, we obtain the following complexity bounds: Single-message broadcast, using the basic abstract MAC layer, takes time O(D log(n/epsilon) log(Delta)) to deliver the message everywhere with probability 1 - epsilon, where D is the network diameter, n is the number of nodes, and Delta is the maximum node degree. Single-message broadcast, using the probabilistic abstract MAC layer, takes time only O((D + log(n/epsilon)) log(Delta)). For multi-message broadcast, the bounds are O((D + k' Delta) log(n/epsilon) log(Delta)) using the basic layer and O((D + k' Delta log(n/epsilon)) log(Delta)) using the probabilistic layer,for the time to deliver a single message everywhere in the presence of at most k' concurrent messages

Erasure Correction for Noisy Radio Networks

The radio network model is a well-studied model of wireless, multi-hop networks. However, radio networks make the strong assumption that messages are delivered deterministically. The recently introduced noisy radio network model relaxes this assumption by dropping messages independently at random. In this work we quantify the relative computational power of noisy radio networks and classic radio networks. In particular, given a non-adaptive protocol for a fixed radio network we show how to reliably simulate this protocol if noise is introduced with a multiplicative cost of poly(log Delta, log log n) rounds where n is the number nodes in the network and Delta is the max degree. Moreover, we demonstrate that, even if the simulated protocol is not non-adaptive, it can be simulated with a multiplicative O(Delta log ^2 Delta) cost in the number of rounds. Lastly, we argue that simulations with a multiplicative overhead of o(log Delta) are unlikely to exist by proving that an Omega(log Delta) multiplicative round overhead is necessary under certain natural assumptions