Relative complexity of programming systems

Issued as Final report, Project no. G-36-62

Theory of systems of asynchronous parallel processors

Issued as Progress report and Final report, Project no. G-36-63

Modeling radio networks

We describe a modeling framework and collection of foundational composition results for the study of probabilistic distributed algorithms in synchronous radio networks. Though the radio setting has been studied extensively by the distributed algorithms community, their results rely on informal descriptions of the channel behavior and therefore lack easy comparability and are prone to error caused by definition subtleties. Our framework rectifies these issues by providing: (1) a method to precisely describe a radio channel as a probabilistic automaton; (2) a mathematical notion of implementing one channel using another channel, allowing for direct comparisons of channel strengths and a natural decomposition of problems into implementing a more powerful channel and solving the problem on the powerful channel; (3) a mathematical definition of a problem and solving a problem; (4) a pair of composition results that simplify the tasks of proving properties about channel implementation algorithms and combining problems with channel implementations. Our goal is to produce a model streamlined for the needs of the radio network algorithms community

Special issue on DISC 2010

This special issue of Distributed Computing is based on papers that originally appeared as extended abstracts in the Proceedings of the 24th International Symposium on Distributed Computing (DISC2010), held in Cambridge, Massachusetts on August 13–15, 2010. The papers for the Special Issue were chosen by the Program Committee from the 32 regular papers presented at the Symposium, based on their quality and representation of the spectrum of topics encompassed by the Symposium. In addition to being reviewed, in preliminary form, by the Program Committee, the full papers submitted for the Special Issue were refereed according to the standard practices of Distributed Computing (due to time constrains, some papers could not appear in this volume). We thank the Members of the Editorial Board for their work in editing this issue, and the referees and the authors of these papers for their respective contributions

Engineering the Virtual Node Layer for Reactive MANET Routing

The VNLayer approach simplifies software development for MANET by providing the developers an abstraction of a network divided into fixed geographical regions, each containing a virtual server for network services. In this paper, we present our study on reactive MANET routing over the VNLayer. During this research, we identified in our initial VNLayer implementation three major limitations that lead to heavy control traffic, long forwarding paths and frequent message collisions in MANET routing. To address the problems, we changed the assumptions made by the VNLayer on the link layer and extended the operations allowed by VNLayer. This results in a VNLayer implementation that can be tuned to optimize the performance of traffic intensive applications (such as routing) while maintaining their simplicity and robustness. Simulation results showed that VNAODV, a VNLayer based routing protocol adapted from AODV, delivers more packets, generates less routing traffic and creates more stable routes than AODV in a dense MANET with high node motion rates. This research validated that the VNLayer approach makes software development for MANET easier and improves the performance of MANET protocols

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

The cost of radio network broadcast for different models of unreliable links

We study upper and lower bounds for the global and local broadcast problems in the dual graph model combined with different strength adversaries. The dual graph model is a generalization of the standard graph-based radio network model that includes unreliable links controlled by an adversary. It is motivated by the ubiquity of unreliable links in real wireless networks. Existing results in this model [11, 12, 3, 8] assume an offline adaptive adversary - the strongest type of adversary considered in standard randomized analysis. In this paper, we study the two other standard types of adversaries: online adaptive and oblivious. Our goal is to find a model that captures the unpredictable behavior of real networks while still allowing for efficient broadcast solutions. For the online adaptive dual graph model, we prove a lower bound that shows the existence of constant-diameter graphs in which both types of broadcast require Ω(n/ log n) rounds, for network size n. This result is within log-factors of the (near) tight upper bound for the offline adaptive setting. For the oblivious dual graph model, we describe a global broadcast algorithm that solves the problem in O(Dlog n + log[superscript 2] n) rounds for network diameter D, but prove a lower bound of Ω(√n= log n) rounds for local broadcast in this same setting. Finally, under the assumption of geographic constraints on the network graph, we describe a local broadcast algorithm that requires only O(log[superscript 2] n logΔ) rounds in the oblivious model, for maximum degree Δ. In addition to the theoretical interest of these results, we argue that the oblivious model (with geographic constraints) captures enough behavior of real networks to render our efficient algorithms useful for real deployments.Ford Motor Company (University Research Program)United States. Air Force Office of Scientific Research (AFOSR Contract No. FA9550- 13-1-0042)National Science Foundation (U.S.) (NSF Award No. CCF-1217506)National Science Foundation (U.S.) (NSF Award No. 0939370-CCF)National Science Foundation (U.S.) (NSF Award No. CCF-AF-0937274)United States. Air Force Office of Scientific Research (AFOSR Contract No. FA9550-08-1-0159)National Science Foundation (U.S.) (NSF Award No. CCF-072651

Relativization of the theory of computational complexity.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1972.Vita.Bibliography: leaves 123-124.Ph.D

Structuring Unreliable Radio Networks

In this paper we study the problem of building a connected dominating set with constant degree (CCDS) in the dual graph radio network model [4,9,10]. This model includes two types of links: reliable, which always deliver messages, and unreliable, which sometimes fail to deliver messages. Real networks compensate for this differing quality by deploying low-layer detection protocols to filter unreliable from reliable links. With this in mind, we begin by presenting an algorithm that solves the CCDS problem in the dual graph model under the assumption that every process u is provided a local link detector set consisting of every neighbor connected to u by a reliable link. The algorithm solves the CCDS problem in O(Δ\log[superscript 2] n/b + log[superscript 3] n) rounds, with high probability, where Δ is the maximum degree in the reliable link graph, n is the network size, and b is an upper bound in bits on the message size. The algorithm works by first building a Maximal Independent Set (MIS) in log[superscript 3] n time, and then leveraging the local topology knowledge to efficiently connect nearby MIS processes. A natural follow up question is whether the link detector must be perfectly reliable to solve the CCDS problem. With this in mind, we first describe an algorithm that builds a CCDS in O(Δpolylog(n)) time under the assumption of O(1) unreliable links included in each link detector set. We then prove this algorithm to be (almost) tight by showing that the possible inclusion of only a single unreliable link in each process's local link detector set is sufficient to require Ω(Δ) rounds to solve the CCDS problem, regardless of message size. We conclude by discussing how to apply our algorithm in the setting where the topology of reliable and unreliable links can change over time.Simons Foundation. (Postdoctoral Fellows Program)United States. Air Force Office of Scientific Research (Award FA9550-08-1-0159)National Science Foundation (U.S.) (Award CCF-0937274)National Science Foundation (U.S.) (Award CCF-0726514)National Science Foundation (U.S.) (Purdue University) (Science and Technology Center Award 0939370-CCF

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