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Probability Metrics and Recursive Algorithms
"... In this paper it is shown by several examples that probability metrics are a useful tool to study the asymptotic behaviour of (stochastic) recursive algorithms. The basic idea of this approach is to find a `suitable ' probability metric which yields contraction properties of the transformation ..."
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Cited by 50 (9 self)
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In this paper it is shown by several examples that probability metrics are a useful tool to study the asymptotic behaviour of (stochastic) recursive algorithms. The basic idea of this approach is to find a `suitable ' probability metric which yields contraction properties of the transformations describing the limits of the algorithm. In order to demonstrate the wide range of applicability of this contraction method we investigate examples from various fields, some of them have been analyzed already in the literature.
Entropy Computations Via Analytic Depoissonization
 IEEE Trans. Information Theory
, 1998
"... We investigate the basic question of information theory, namely, evaluation of Shannon entropy, and a more general Rényi entropy, for some discrete distributions (e.g., binomial, negative binomial, etc.). We aim at establishing analytic methods (i.e., those in which complex analysis plays a pivotal ..."
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Cited by 36 (12 self)
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We investigate the basic question of information theory, namely, evaluation of Shannon entropy, and a more general Rényi entropy, for some discrete distributions (e.g., binomial, negative binomial, etc.). We aim at establishing analytic methods (i.e., those in which complex analysis plays a pivotal role) for such computations which often yield estimates of unparalleled precision. The main analytic tool used here is that of analytic poissonization and depoissonization. We illustrate our approach on the entropy evaluation of the binomial distribution, that is, we prove that for Binomial(n; p) distribution the entropy h n becomes h n i 1 2 ln n+ 1 2 +ln p 2ßp(1 \Gamma p)+ P k1 a k n \Gammak where a k are explicitly computable constants. Moreover, we shall argue that analytic methods (e.g., complex asymptotics such as Rice's method and singularity analysis, Mellin transforms, poissonization and depoissonization) can offer new tools for information theory, especially for studying ...
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 "bur ..."
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Cited by 23 (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.
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 17 (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
Analysis of Contention TreeAlgorithms
 IEEE Trans. Inform. Theory
, 2000
"... The CapetanakisTsybakovMikhailov contention treealgorithm provides an efficient scheme for multiaccessing a broadcastcommunication channel. This article studies statistical properties of multipleaccess contention treealgorithms with ternary feedback for arbitrary degree of node. The particular ..."
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Cited by 10 (0 self)
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The CapetanakisTsybakovMikhailov contention treealgorithm provides an efficient scheme for multiaccessing a broadcastcommunication channel. This article studies statistical properties of multipleaccess contention treealgorithms with ternary feedback for arbitrary degree of node. The particular quantities under investigation are the number of levels required for a random contender to have successful access, as well as the number of levels and the number of contention frames required to provide access for all contenders. Through classical Fourier analysis approximations to both the average and the variance are calculated as a function of the number of contenders n. It is demonstrated that in the limit of large n these quantities do not converge to a fixed mode, but contain an oscillating term as well.
An analytic approach to the asymptotic variance of trie statistics and related structures
, 2013
"... ..."
Analysis of dynamic tree algorithms
 In preparation
, 2004
"... Abstract. In this paper, a general tree algorithm processing a random flow of arrivals is analyzed. CapetanakisTsybakovMikhailov’s protocol in the context of communication networks with random access is an example of such an algorithm. In computer science, this corresponds to a trie structure with ..."
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Cited by 8 (1 self)
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Abstract. In this paper, a general tree algorithm processing a random flow of arrivals is analyzed. CapetanakisTsybakovMikhailov’s protocol in the context of communication networks with random access is an example of such an algorithm. In computer science, this corresponds to a trie structure with a dynamic input. Mathematically, it is related to a stopped branching process with exogeneous arrivals (immigration). Under quite general assumptions on the distribution of the number of arrivals and on the branching procedure, it is shown that there exists a positive constant λc so that if the arrival rate is smaller than λc, then the algorithm is stable under the flow of requests, i.e. that the total size of an associated tree is integrable. At the same time a gap in the earlier proofs of stability of the literature is fixed. When the arrivals are Poisson, an explicit characterization of λc is given. Under the stability condition, the asymptotic behavior of the average size of a tree starting with a large number of individuals is analyzed. The results are obtained with the help of a probabilistic rewriting of the functional equations describing the dynamic
The Immediate Dependency Relation: an Optimal Way to Ensure Causal Group Communication
 ANNUAL REVIEW OF SCALABLE COMPUTING, EDITIONS WORLD SCIENTIFIC, SERIES ON SCALABLE COMPUTING
, 2004
"... In this paper we present a study on the subject of the Immediate Dependency Relation (IDR), and we show how by extending the IDR relation, one can ensure a global causal delivery in group communication, including in the overlapping group case. The main objective of this paper is to show that the use ..."
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Cited by 7 (0 self)
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In this paper we present a study on the subject of the Immediate Dependency Relation (IDR), and we show how by extending the IDR relation, one can ensure a global causal delivery in group communication, including in the overlapping group case. The main objective of this paper is to show that the use of the Immediate Dependency Relation (IDR) obliterates the notion that causality is expensive to set up in distributed systems. The IDR minimizes considerably the amount of control information sent per message to ensure causal ordering, without imposing restrictions in interaction (e.g. network topology, redifussion servers, executions models etc.). In order to demonstrate the feasibility of its implementation, we present an optimal broadcast causal protocol inspired by the IDR relation. We show the optimality of the protocol in terms of the amount of control information timestamped per message.
Analytic Models For Tree Communication Protocols
, 1987
"... The tree protocol for local area networks, together with a number of its variants, can be exactly analysed under a Poisson arrival model. This note surveys some of the evaluations that have been obtained for characteristic parameters including delay, session length or probability of immediate access ..."
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Cited by 5 (0 self)
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The tree protocol for local area networks, together with a number of its variants, can be exactly analysed under a Poisson arrival model. This note surveys some of the evaluations that have been obtained for characteristic parameters including delay, session length or probability of immediate access to the channel. The mathematical techniques involved are: functional equations and Mellin transforms.
Renewal theory in analysis of tries and strings
, 2009
"... We give a survey of a number of simple applications of renewal theory to problems on random strings and tries: insertion depth, size, insertion mode and imbalance of tries; variations for btries and Patricia tries; Khodak and Tunstall codes. ..."
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Cited by 4 (1 self)
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We give a survey of a number of simple applications of renewal theory to problems on random strings and tries: insertion depth, size, insertion mode and imbalance of tries; variations for btries and Patricia tries; Khodak and Tunstall codes.