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31
Adversarial contention resolution for simple channels
 In: 17th Annual Symposium on Parallelism in Algorithms and Architectures
, 2005
"... This paper analyzes the worstcase performance of randomized backoff on simple multipleaccess channels. Most previous analysis of backoff has assumed a statistical arrival model. For batched arrivals, in which all n packets arrive at time 0, we show the following tight highprobability bounds. Rand ..."
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Cited by 34 (1 self)
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This paper analyzes the worstcase performance of randomized backoff on simple multipleaccess channels. Most previous analysis of backoff has assumed a statistical arrival model. For batched arrivals, in which all n packets arrive at time 0, we show the following tight highprobability bounds. Randomized binary exponential backoff has makespan Θ(nlgn), and more generally, for any constant r, rexponential backoff has makespan Θ(nlog lgr n). Quadratic backoff has makespan Θ((n/lg n) 3/2), and more generally, for r> 1, rpolynomial backoff has makespan Θ((n/lg n) 1+1/r). Thus, for batched inputs, both exponential and polynomial backoff are highly sensitive to backoff constants. We exhibit a monotone superpolynomial subexponential backoff algorithm, called loglogiterated backoff, that achieves makespan Θ(nlg lgn/lg lglgn). We provide a matching lower bound showing that this strategy is optimal among all monotone backoff algorithms. Of independent interest is that this lower bound was proved with a delay sequence argument. In the adversarialqueuing model, we present the following stability and instability results for exponential backoff and loglogiterated backoff. Given a (λ,T)stream, in which at most n = λT packets arrive in any interval of size T, exponential backoff is stable for arrival rates of λ = O(1/lgn) and unstable for arrival rates of λ = Ω(lglgn/lg n); loglogiterated backoff is stable for arrival rates of λ = O(1/(lg lgnlgn)) and unstable for arrival rates of λ = Ω(1/lg n). Our instability results show that bursty input is close to being worstcase for exponential backoff and variants and that even small bursts can create instabilities in the channel.
On Contention Resolution Protocols and Associated Probabilistic Phenomena
 IN PROCEEDINGS OF THE 26TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING
, 1994
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Conflict resolution algorithms and their performance analysis
, 1993
"... Multiple Access protocols are distributed algorithms that enable a set of geographically dispersed stations to communicate using a single, common, broadcast channel. We concentrate on the class of Conflict Resolution Algorithms. This class exhibits very good performance characteristics for ‘‘bursty’ ..."
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Cited by 21 (0 self)
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Multiple Access protocols are distributed algorithms that enable a set of geographically dispersed stations to communicate using a single, common, broadcast channel. We concentrate on the class of Conflict Resolution Algorithms. This class exhibits very good performance characteristics for ‘‘bursty’ ’ computer communications traffic, including high capacity, low delay under light traffic conditions, and inherent stability. One algorithm in this class achieves the highest capacity among all known multipleaccess protocols for the infinite population Poisson model. Indeed, this capacity is not far from a theoretical upper bound. After surveying the most important and influential Conflict Resolution Algorithms, the emphasis in our presentation is shifted to methods for their analysis and results of their performance evaluation. We also discuss some extensions of the basic protocols and performance results for nonstandard environments, such as Local Area Networks, satellite channels, channels with errors, etc., providing a comprehensive bibliography. 1. Conflict Resolution Based Random Access Protocols The ALOHA protocols were a breakthrough in the area of multiple access communications. 1 They delivered, more or less, what they advertized, i.e., low delay for bursty, computer generated traffic. They suffer, however, from stability problems and low capacity. 2 The next major breakthrough in the area of multiple access communications
Adversarial queuing on the multipleaccess channel
 In Proc. of PODC ’06
, 2006
"... We consider broadcasting on the multipleaccess channel when packets are injected continuously. Multipleaccess channel is a synchronous system with the properties that a single transmission at a round delivers the message to all nodes, while multiple simultaneous transmissions result in a conflict ..."
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Cited by 17 (8 self)
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We consider broadcasting on the multipleaccess channel when packets are injected continuously. Multipleaccess channel is a synchronous system with the properties that a single transmission at a round delivers the message to all nodes, while multiple simultaneous transmissions result in a conflict which prevents delivering messages to any among the recipients. The traditional approach to dynamic broadcasting has been concerned with stability of protocols under suitable stochastic assumptions about injection rates. We study deterministic protocols competing against adversaries restricted by injection rate and burstiness of traffic. Stability means that the number of packets in queues is bounded by a constant in any execution, for a given number of stations, protocol, and adversary. Strong stability denotes the
Randomized communication in radio networks
 HANDBOOK OF RANDOMIZED COMPUTING
, 2001
"... A communication network is called a radio network if its nodes exchange messages in the following restricted way. First, a send operation performed by a node delivers copies of the same message to all directly reachable nodes. Secondly, a node can successfully receive an incoming message only if exa ..."
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Cited by 14 (0 self)
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A communication network is called a radio network if its nodes exchange messages in the following restricted way. First, a send operation performed by a node delivers copies of the same message to all directly reachable nodes. Secondly, a node can successfully receive an incoming message only if exactly one of its neighbors sent a message in that step. It is this semantics of how ports at nodes send and receive messages that defines the networks rather than the fact that only radio waves are used as a medium of communication; but if that is the case then just a single frequency is used. We discuss algorithmic aspects of exchanging information in such networks, concentrating on distributed randomized protocols. Specific problems and solutions depend a lot on the topology of the underlying reachability graph and how much the nodes know about it. In singlehop networks each pair of nodes can communicate directly. This kind of networks is also known as the multiple access channel. Popular
A.: Leader election in ad hoc radio networks: A keen ear helps
 In: Proceedings of the 36th International Colloquium on Automata, Languages and Programming (ICALP), Part II
, 2009
"... Abstract. We address the fundamental distributed problem of leader election in ad hoc radio networks modeled as undirected graphs. Nodes are stations having distinct integer labels, and each node knows only its own label and a polynomial upper bound on all labels. A signal from a transmitting node r ..."
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Cited by 10 (4 self)
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Abstract. We address the fundamental distributed problem of leader election in ad hoc radio networks modeled as undirected graphs. Nodes are stations having distinct integer labels, and each node knows only its own label and a polynomial upper bound on all labels. A signal from a transmitting node reaches all neighbors. What distinguishes radio networks from messagepassing networks is that a message is received successfully by a node, if and only if, exactly one of its neighbors transmits in this round. If two neighbors of a node transmit simultaneously in a given round, none of the messages is heard by the receiving node. In this case we say that a collision occurred at this node. An important capability of nodes of a radio network is collision detection:the ability of nodes to distinguish a collision from the background noise occurring when no neighbor transmits. (This ability is the “keen ear ” of the nodes.) Can collision detection speed up leader election in arbitrary radio networks? We give a positive answer to this question. More precisely, our main result is a deterministic leader election algorithm working in time O(n) in all nnode networks, if collision detection is available, while it is known that deterministic leader election requires time Ω(nlog n), even for complete networks, if there is no collision detection. This is the first computational task whose execution for arbitrary radio networks is shown to be faster with collision detection than without it. 1
Consensus and mutual exclusion in a multiple access channel
 IEEE Transactions on Parallel and Distributed Systems
"... Abstract. We consider deterministic feasibility and time complexity of two fundamental tasks in distributed computing: consensus and mutual exclusion. Processes have different labels and communicate through a multiple access channel. The adversary wakes up some processes in possibly different rounds ..."
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Cited by 7 (3 self)
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Abstract. We consider deterministic feasibility and time complexity of two fundamental tasks in distributed computing: consensus and mutual exclusion. Processes have different labels and communicate through a multiple access channel. The adversary wakes up some processes in possibly different rounds. In any round every awake process either listens or transmits. The message of a process i is heard by all other awake processes, if i is the only process to transmit in a given round. If more than one process transmits simultaneously, there is a collision and no message is heard. We consider three characteristics that may or may not exist in the channel: collision detection (listening processes can distinguish collision from silence), the availablity of a global clock showing the round number, and the knowledge of the number n of all processes. If none of the above three characteristics is available in the channel, we prove that consensus and mutual exclusion are infeasible; if at least one of them is available, both tasks are feasible and we study their time complexity. Collision detection is shown to cause an exponential gap in complexity: if it is available, both tasks can be performed in time logarithmic in n, which is optimal, and without collision detection both tasks require linear time. We then investigate both consensus and mutual exclusion in the absence of collision detection, but under alternative presence of the two other features. With global clock, we give an algorithm whose time complexity linearly depends on n and on the wakeup time, and an algorithm whose complexity does not depend on the wakeup time and differs from the linear lower bound only by a factor O(log 2 n). If n is known, we also show an algorithm whose complexity differs from the linear lower bound only by a factor O(log 2 n).
Straggler identification in roundtrip data streams via Newton’s identities and invertible Bloom filters
 IEEE Transactions on Knowledge and Data Engineering
, 2011
"... Abstract. We study the straggler identification problem, in which an algorithm must determine the identities of the remaining members of a set after it has had a large number of insertion and deletion operations performed on it, and now has relatively few remaining members. The goal is to do this in ..."
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Cited by 7 (1 self)
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Abstract. We study the straggler identification problem, in which an algorithm must determine the identities of the remaining members of a set after it has had a large number of insertion and deletion operations performed on it, and now has relatively few remaining members. The goal is to do this in o(n) space, where n is the total number of identities. Straggler identification has applications, for example, in determining the unacknowledged packets in a highbandwidth multicast data stream. We provide a deterministic solution to the straggler identification problem that uses only O(d log n) bits, based on a novel application of Newton’s identities for symmetric polynomials. This solution can identify any subset of d stragglers from a set of n O(log n)bit identifiers, assuming that there are no false deletions of identities not already in the set. Indeed, we give a lower bound argument that shows that any smallspace deterministic solution to the straggler identification problem cannot be guaranteed to handle false deletions. Nevertheless, we provide a simple randomized solution using O(d log nlog(1/ǫ)) bits that can maintain a multiset and solve the straggler identification problem, tolerating false deletions, where ǫ> 0 is a userdefined parameter bounding the probability of an incorrect response. This randomized solution is based on a new type of Bloom filter, which we call the invertible Bloom filter.
The DoAll Problem in Broadcast Networks
, 2001
"... The problem of performing t tasks in a distributed system on p failureprone processors is one of the fundamental problems in distributed computing. If the tasks are similar and independent and the processors communicate by sending messages then the problem is called DoAll . In our work the communi ..."
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Cited by 6 (4 self)
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The problem of performing t tasks in a distributed system on p failureprone processors is one of the fundamental problems in distributed computing. If the tasks are similar and independent and the processors communicate by sending messages then the problem is called DoAll . In our work the communication is over a multipleaccess channel, and the attached stations may fail by crashing. The measure of performance is work, defined as the number of the available processor steps. Algorithms are required to be reliable in that they perform all the tasks as long as at least one station remains operational. We show that each reliable algorithm always needs to perform at least the minimum amount t + p p t) of work. We develop an optimal deterministic algorithm for the channel with collision detection performing only the minimum work (t + p p t). Another algorithm is given for the channel without collision detection, it performs work O(t+p p t+p minff; tg), where f < p is the number of failures. It is proved to be optimal if the number of faults is the only restriction on the adversary. Finally we consider the question if randomization helps for the channel without collision detection against weaker adversaries. We develop a randomized algorithm which needs to perform only the expected minimum work if the adversary may fail a constant fraction of stations, but it has to select the failureprone stations prior to the start of an algorithm.
What Is the Use of Collision Detection (in Wireless Networks)?
"... We show that the asymptotic gain in the time complexity when using collision detection depends heavily on the task by investigating three prominent problems for wireless networks, i.e. the maximal independent set (MIS), broadcasting and coloring problem. We present lower and upper bounds for all thr ..."
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Cited by 6 (0 self)
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We show that the asymptotic gain in the time complexity when using collision detection depends heavily on the task by investigating three prominent problems for wireless networks, i.e. the maximal independent set (MIS), broadcasting and coloring problem. We present lower and upper bounds for all three problems for the GrowthBounded Graph such as the Unit Disk Graph. We prove that the benefit of collision detection ranges from an exponential improvement down to no asymptotic gain at all. In particular, for the broadcasting problem our deterministic algorithm is running in time O(D log n). It is an exponential improvement over prior work, if the diameter D is polylogarithmic in the number of nodes n, i.e. D ∈ O(log c n) for some constant c. 1