We consider broadcasting in radio networks, modeled as unit disk graphs (UDG). Such networks occur in wireless communication between sites (e.g., stations or sensors) situated in a terrain. Network stations are represented by points in the Euclidean plane, where a station is connected to all stations at distance at most 1 from it. A message transmitted by a station reaches all its neighbors, but a station hears a message (receives the message correctly) only if exactly one of its neighbors transmits at a given time step. One station of the network, called the source, has a message which has to be disseminated to all other stations. Stations are unaware of the network topology. Two broadcasting models are considered. In the conditional wake up model, the stations other than the source are initially idle and cannot transmit until they hear a message for the first time. In the spontaneous wake up model, all stations are awake (and may transmit messages) from the beginning.It turns out that broadcasting time depends on two parameters of the UDG network, namely, its diameter D and its granularity g, which is the inverse of the minimum dis- * tance between any two stations. We present a deterministic broadcasting algorithm which works in time O(Dg) under the conditional wake up model and prove that broadcasting in this model cannot be accomplished by any deterministic algorithm in time better than Ω(D √ g). For the spontaneous wake up model, we design two deterministic broadcasting algorithms: the first works in time O(D + g 2 ) and the second in time O(D log g). While none of these algorithms alone is optimal for all parameter values, we prove that the algorithm obtained by interleaving their steps, and thus working in time O`min˘D + g 2 , D log g¯´, turns out to be optimal by establishing a matching lower bound.

In this paper we study the topological properties of wireless communication maps and their usability in algorithmic design. We consider the SINR model, which compares the received power of a signal at a receiver against the sum of strengths of other interfering signals plus background noise. To describe the behavior of a multi-station network, we use the convenient representation of a reception map. In the SINR model, the resulting SINR diagram partitions the plane into reception zones, one per station, and the complementary region of the plane where no station can be heard. SINR diagrams have been studied in [3] for the specific case where all stations use the same power. It is shown that the reception zones are convex (hence connected) and fat, and this is used to devise an efficient algorithm for the fundamental problem of point location. Here we consider the more general (and common) case where transmission energies are arbitrary (or non-uniform). Under that setting, the reception zones are not necessarily convex or even connected. This poses the algorithmic challenge of designing efficient point location techniques for the non-uniform setting, as well as the theoretical challenge of understanding the geometry of SINR diagrams (e.g., the maximal number of connected components they might have). We achieve several results in both directions. We establish a form of weaker convexity in the case where stations are aligned on a line and use this to derive a tight bound on the number of connected components in this case. In addition, one of our key results concerns the behavior of a (d + 1)-dimensional * A full version of the paper is available at , i.e., a map in one dimension higher than the dimension in which stations are embedded. Specifically, although the d-dimensional map might be highly fractured, drawing the map in one dimension higher "heals" the zones, which become connected (in fact hyperbolically connected). In addition, as a step toward establishing a weaker form of convexity for the d-dimensional map, we study the interference function and show that it satisfies the maximum principle. This is done through an analysis technique based on looking at the behavior of systems composed on lines of densely placed weak stations, as the number of stations tends to infinity, keeping their total transmission energy fixed. Finally, we turn to consider algorithmic applications, and propose a new variant of approximate point location.

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. IntroductionMost existing work on distributed algorithms for wireless networks assumes low-level synchronous models that require algorithms to deal directly with link-layer issues such as signal fading (e.g., [22,20,13]) and contention (e.g., [2, 16, 28, 12]). These low-level models are appropriate for answering basic science questions about the capabilities and limits of wireless communication. We argue, however, that they are often not appropriate for designing and analyzing algorithms meant for real world deployment, because: (1) they fail to capture the unpredictable reality of real radio signal propagation (which tends not to follow simple collision or fading rules [33]); (2) they do not address issues like network co-existence (it is rarely true that your algorithm is alone in using the wireless channel); and (3) they ignore the presence of general purpose MAC layers which are standard and hard to bypass in existing devices. * Supported in a part by AFOSR FA9550-13-1-0042 and NSF grants Nos. CCF-0939370, CCF-1217506, and CCF-AF-0937274. 1In [29,30], we introduced the abstract MAC layer approach as an alternative to low-level models for studying wireless algorithms. This approach moves the algorithm designer up the network stack by modeling the basic guarantees of most existing wireless MAC layers. In doing so, it abstracts away low level issues such as signal fading and contention, instead capturing the impact of this behavior on higher layers with model uncertainty. Because abstract MAC layers are defined to maintain the basic guarantees of most standard wireless MAC layers, algorithms developed in such models can be deployed on existing devices while maintaining their formally proved properties.In this paper, we study the basic communication primitive of mult...

Many modern datacenter applications involve large-scale computations composed of multiple data flows that need to be completed over a shared set of distributed resources. Such a computation completes when all of its flows complete. A useful abstraction for modeling such scenarios is a coflow, which is a collection of flows (e.g., tasks, packets, data transmissions) that all share the same performance goal.In this paper, we present the first approximation algorithms for scheduling coflows over general network topologies with the objective of minimizing total weighted completion time. We consider two different models for coflows based on the nature of individual flows: circuits, and packets. We design constant-factor polynomial-time approximation algorithms for scheduling packet-based coflows with or without given flow paths, and circuit-based coflows with given flow paths. Furthermore, we give an O(log n/ log log n)approximation polynomial time algorithm for scheduling circuitbased coflows where flow paths are not given (here n is the number of network edges).We obtain our results by developing a general framework for coflow schedules, based on interval-indexed linear programs, which may extend to other coflow models and objective functions and may also yield improved approximation bounds for specific network scenarios. We also present an experimental evaluation of our approach for circuit-based coflows that show a performance improvement of at least %22 on average over competing heuristics.

The rules governing the availability and quality of connections in a wireless network are described by physical models such as the signal-to-interference & noise ratio (SINR) model. For a collection of simultaneously transmitting stations in the plane, it is possible to identify a reception zone for each station, consisting of the points where its transmission is received correctly. The resulting SINR diagram partitions the plane into a reception zone per station and the remaining plane where no station can be heard. SINR diagrams appear to be fundamental to understanding the behavior of wireless networks, and may play a key role in the development of suitable algorithms for such networks, analogous perhaps to the role played by Voronoi diagrams in the study of proximity queries and related issues in computational geometry. So far, however, the properties of SINR diagrams have not been studied systematically, and most algorithmic studies in wireless networking rely on simplified graph-based models such as the unit disk graph (UDG) model, which conveniently abstract away interference-related complications, and make it easier to handle algorithmic issues, but consequently fail to capture accurately some important aspects of wireless networks. This article focuses on obtaining some basic understanding of SINR diagrams, their properties and their usability in algorithmic applications. Specifically, we have shown that assuming uniform power transmissions, the reception zones are convex and relatively well-rounded. These results are then used to develop an efficient approximation algorithm for a fundamental point location problem in wireless networks.