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Supporting Stored Video: Reducing Rate Variability and EndtoEnd Resource Requirements through Optimal Smoothing
 IEEE/ACM Transactions on Networking
, 1998
"... Variablebitrate compressed video can exhibit significant, multipletimescale bit rate variability. In this paper we consider the transmission of stored video from a server to a client across a network, and explore how the client buffer space can be used most effectively toward reducing the variab ..."
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Cited by 219 (17 self)
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Variablebitrate compressed video can exhibit significant, multipletimescale bit rate variability. In this paper we consider the transmission of stored video from a server to a client across a network, and explore how the client buffer space can be used most effectively toward reducing the variability of the transmitted bit rate. Two basic results are presented. First, we show how to achieve the greatest possible reduction in rate variability when sending stored video to a client with given buffer size. We formally establish the optimality of our approach and illustrate its performance over a set of long MPEG1 encoded video traces. Second, we evaluate the impact of optimal smoothing on the network resources needed for video transport, under two network service models: Deterministic Guaranteed service [1, 31] and Renegotiated CBR (RCBR) service [9]. Under both models the impact of optimal smoothing is dramatic. 1 Introduction A broad range of applications is enabled by the capac...
Wavelet Analysis of Long Range Dependent Traffic
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A Wavelet based tool for the analysis of long range dependence is introduced and a related semiparametric estimator of the Hurst parameter. The estimator is shown to be unbiased under very general conditions, and efficient under Gaussian assumptions. It can be implemented very efficiently allowing t ..."
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Cited by 216 (16 self)
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A Wavelet based tool for the analysis of long range dependence is introduced and a related semiparametric estimator of the Hurst parameter. The estimator is shown to be unbiased under very general conditions, and efficient under Gaussian assumptions. It can be implemented very efficiently allowing the direct analysis of very large data sets, and is highly robust against the presence of deterministic trends, as well as allowing their detection and identification. Statistical, computational and numerical comparisons are made against traditional estimators including that of Whittle. The estimator is used to perform a thorough analysis of the long range dependence in Ethernet traffic traces. New features are found with important implications for the choice of valid models for performance evaluation. A study of mono vs multifractality is also performed, and a preliminary study of the stationarity with respect to the Hurst parameter and deterministic trends.
A Logic for Reasoning about Probabilities
 Information and Computation
, 1990
"... We consider a language for reasoning about probability which allows us to make statements such as “the probability of E, is less than f ” and “the probability of E, is at least twice the probability of E,, ” where E, and EZ are arbitrary events. We consider the case where all events are measurable ( ..."
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Cited by 214 (19 self)
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We consider a language for reasoning about probability which allows us to make statements such as “the probability of E, is less than f ” and “the probability of E, is at least twice the probability of E,, ” where E, and EZ are arbitrary events. We consider the case where all events are measurable (i.e., represent measurable sets) and the more general case, which is also of interest in practice, where they may not be measurable. The measurable case is essentially a formalization of (the propositional fragment of) Nilsson’s probabilistic logic. As we show elsewhere, the general (nonmeasurable) case corresponds precisely to replacing probability measures by DempsterShafer belief functions. In both cases, we provide a complete axiomatization and show that the problem of deciding satistiability is NPcomplete, no worse than that of propositional logic. As a tool for proving our complete axiomatizations, we give a complete axiomatization for reasoning about Boolean combinations of linear inequalities, which is of independent interest. This proof and others make crucial use of results from the theory of linear programming. We then extend the language to allow reasoning about conditional probability and show that the resulting logic is decidable and completely axiomatizable, by making use of the theory of real closed fields. ( 1990 Academic Press. Inc 1.
Proof of a Fundamental Result in SelfSimilar Traffic Modeling
 COMPUTER COMMUNICATION REVIEW
, 1997
"... We state and prove the following key mathematical result in selfsimilar traffic modeling: the superposition of many ON/OFF sources (also known as packet trains) with strictly alternating ON and OFFperiods and whose ONperiods or OFFperiods exhibit the Noah Effect (i.e., have high variability or ..."
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Cited by 206 (8 self)
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We state and prove the following key mathematical result in selfsimilar traffic modeling: the superposition of many ON/OFF sources (also known as packet trains) with strictly alternating ON and OFFperiods and whose ONperiods or OFFperiods exhibit the Noah Effect (i.e., have high variability or infinite variance) can produce aggregate network traffic that exhibits the Joseph Effect (i.e., is selfsimilar or longrange dependent). There is, moreover, a simple relation between the parameters describing the intensities of the Noah Effect (high variability) and the Joseph Effect (selfsimilarity). This provides a simple physical explanation for the presence of selfsimilar traffic patterns in modern highspeed network traffic that is consistent with traffic measurements at the source level. We illustrate how this mathematical result can be combined with modern highperformance computing capabilities to yield a simple and efficient lineartime algorithm for generating selfsimilar traf...
On the computation of multidimensional aggregates
 IN PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON VERY LARGE DATABASES
, 1996
"... At the heart of all OLAP or multidimensional data analysis applications is the ability to simultaneously aggregate across many sets of dimensions. Computing multidimensional aggregates is a performance bottleneck for these applications. This paper presents fast algorithms for computing a collection ..."
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Cited by 205 (18 self)
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At the heart of all OLAP or multidimensional data analysis applications is the ability to simultaneously aggregate across many sets of dimensions. Computing multidimensional aggregates is a performance bottleneck for these applications. This paper presents fast algorithms for computing a collection of groupbys. We focus on a special case of the aggregation problem  computation of the CUBE operator. The CUBE operator requires computing groupbys on all possible combinations of a list of attributes, and is equivalent to the union of a number of standard groupby operations. We show howthe structure of CUBE computation can be viewed in terms of a hierarchy of groupby operations. Our algorithms extend sortbased and hashbased grouping methods with several optimizations, like combining common operations across multiple groupbys, caching, and using precomputed groupbys for computing other groupbys. Empirical evaluation shows that the resulting algorithms give much better performance compared to straightforward methods. This paper combines work done concurrently on computing the data cube by two different teams as reported in [SAG96] and [DANR96].
Expander Graphs and their Applications
, 2003
"... Contents 1 The Magical Mystery Tour 7 1.1 Some Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.1 Hardness results for linear transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.2 Error Correcting Codes . . . . . . . ..."
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Cited by 188 (5 self)
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Contents 1 The Magical Mystery Tour 7 1.1 Some Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.1 Hardness results for linear transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.2 Error Correcting Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.1.3 Derandomizing Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Magical Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2.1 A Super Concentrator with O(n) edges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2.2 Error Correcting Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2.3 Derandomizing Random Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
On the Analysis of the (1+1) Evolutionary Algorithm
 THEORETICAL COMPUTER SCIENCE
, 2002
"... Many experimental results are reported on all types of Evolutionary Algorithms but only few results have been proved. A step towards a theory on Evolutionary Algorithms, in particular, the socalled (1 + 1) Evolutionary Algorithm, is performed. Linear functions are proved to be optimized in expected ..."
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Cited by 184 (41 self)
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Many experimental results are reported on all types of Evolutionary Algorithms but only few results have been proved. A step towards a theory on Evolutionary Algorithms, in particular, the socalled (1 + 1) Evolutionary Algorithm, is performed. Linear functions are proved to be optimized in expected time O(n ln n) but only mutation rates of size #(1/n) can ensure this behavior. For some polynomial of degree 2 the optimization needs exponential time. The same is proved for a unimodal function. Both results were not expected by several other authors. Finally, a hierarchy result is proved. Moreover, methods are presented to analyze the behavior of the (1 + 1) Evolutionary Algorithm.
Effective bandwidths at multiclass queues
 Queueing Systems
, 1991
"... Consider a queue which serves traffic from a number of distinct sources and which is required to deliver a performance guarantee, expressed in terms of the mean delay or the probability the delay exceeds a threshold. For various simple models we show that an effective bandwidth can be associated wit ..."
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Cited by 182 (4 self)
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Consider a queue which serves traffic from a number of distinct sources and which is required to deliver a performance guarantee, expressed in terms of the mean delay or the probability the delay exceeds a threshold. For various simple models we show that an effective bandwidth can be associated with each source, and that the queue can deliver its performance guarantee by limiting the sources served so that their effective bandwidths sum to less than the capacity of the queue. Keywords: large deviations, M/G/1 queue, circuitswitched network, connection acceptance control. 1.
Approximate graph coloring by semidefinite programming
 Proc. 35 th IEEE FOCS, IEEE
, 1994
"... a coloring is called the chromatic number of�, and is usually denoted by��.Determining the chromatic number of a graph is known to be NPhard (cf. [19]). Besides its theoretical significance as a canonical NPhard problem, graph coloring arises naturally in a variety of applications such as register ..."
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Cited by 180 (7 self)
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a coloring is called the chromatic number of�, and is usually denoted by��.Determining the chromatic number of a graph is known to be NPhard (cf. [19]). Besides its theoretical significance as a canonical NPhard problem, graph coloring arises naturally in a variety of applications such as register allocation [11, 12, 13] is the maximum degree of any vertex. Beand timetable/examination scheduling [8, 40]. In many We consider the problem of coloring�colorable graphs with the fewest possible colors. We give a randomized polynomial time algorithm which colors a 3colorable graph on vertices with� � ���� colors where sides giving the best known approximation ratio in terms of, this marks the first nontrivial approximation result as a function of the maximum degree. This result can be generalized to�colorable graphs to obtain a coloring using�� � ��� � � � �colors. Our results are inspired by the recent work of Goemans and Williamson who used an algorithm for semidefinite optimization problems, which generalize linear programs, to obtain improved approximations for the MAX CUT and MAX 2SAT problems. An intriguing outcome of our work is a duality relationship established between the value of the optimum solution to our semidefinite program and the Lovász�function. We show lower bounds on the gap between the optimum solution of our semidefinite program and the actual chromatic number; by duality this also demonstrates interesting new facts about the�function. 1
Random Walks in PeertoPeer Networks
, 2004
"... We quantify the effectiveness of random walks for searching and construction of unstructured peertopeer (P2P) networks. For searching, we argue that random walks achieve improvement over flooding in the case of clustered overlay topologies and in the case of reissuing the same request several tim ..."
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Cited by 177 (2 self)
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We quantify the effectiveness of random walks for searching and construction of unstructured peertopeer (P2P) networks. For searching, we argue that random walks achieve improvement over flooding in the case of clustered overlay topologies and in the case of reissuing the same request several times. For construction, we argue that an expander can be maintained dynamically with constant operations per addition. The key technical ingredient of our approach is a deep result of stochastic processes indicating that samples taken from consecutive steps of a random walk can achieve statistical properties similar to independent sampling (if the second eigenvalue of the transition matrix is bounded away from 1, which translates to good expansion of the network; such connectivity is desired, and believed to hold, in every reasonable network and network model). This property has been previously used in complexity theory for construction of pseudorandom number generators. We reveal another facet of this theory and translate savings in random bits to savings in processing overhead.