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Phase transition for parking blocks, Brownian excursion and coalescence
, 2005
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Analysis of Methods for Scheduling Low Priority Disk Drive Tasks
 Proc. ACM SIGMETRICS
, 2002
"... This paper analyzes various algorithms for scheduling low priority disk drive tasks. The derived closed form solution is applicable to class of greedy algorithms that include a variety of background disk scanning applications. By paying close attention to many characteristics of modern disk drives, ..."
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Cited by 23 (1 self)
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This paper analyzes various algorithms for scheduling low priority disk drive tasks. The derived closed form solution is applicable to class of greedy algorithms that include a variety of background disk scanning applications. By paying close attention to many characteristics of modern disk drives, the analytical solutions achieve very high accuracythe difference between the predicted response times and the measurements on two different disks is only 3% for all but one examined workload. This paper also proves a theorem which shows that background tasks implemented by greedy algorithms can be accomplished with very little seek penalty. Using greedy algorithm gives a 10% shorter response time for the foreground application requests and up to a 20% decrease in total background task run time compared to results from previously published techniques.
On the Analysis of Linear Probing Hashing
, 1998
"... This paper presents moment analyses and characterizations of limit distributions for the construction cost of hash tables under the linear probing strategy. Two models are considered, that of full tables and that of sparse tables with a fixed filling ratio strictly smaller than one. For full tables, ..."
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Cited by 23 (8 self)
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This paper presents moment analyses and characterizations of limit distributions for the construction cost of hash tables under the linear probing strategy. Two models are considered, that of full tables and that of sparse tables with a fixed filling ratio strictly smaller than one. For full tables, the construction cost has expectation O(n3/2), the standard deviation is of the same order, and a limit law of the Airy type holds. (The Airy distribution is a semiclassical distribution that is defined in terms of the usual Airy functions or equivalently in terms of Bessel functions of indices − 1 2 3, 3.) For sparse tables, the construction cost has expectation O(n), standard deviation O ( √ n), and a limit law of the Gaussian type. Combinatorial relations with other problems leading to Airy phenomena (like graph connectivity, tree inversions, tree path length, or area under excursions) are also briefly discussed.
Parking Functions, Empirical Processes, and the Width of Rooted Labeled Trees
"... This paper provides tight bounds for the moments of the width of rooted labeled trees with n nodes, answering an open question of Odlyzko and Wilf (1987). To this aim, we use one of the many onetoone correspondences between trees and parking functions, and also a precise coupling between parking f ..."
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Cited by 19 (6 self)
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This paper provides tight bounds for the moments of the width of rooted labeled trees with n nodes, answering an open question of Odlyzko and Wilf (1987). To this aim, we use one of the many onetoone correspondences between trees and parking functions, and also a precise coupling between parking functions and the empirical processes of mathematical statistics. Our result turns out to be a consequence of the strong convergence of empirical processes to the Brownian bridge (Komlos, Major and Tusnady, 1975).
Ephemeral Networks with Random Availability of Links: Diameter and Connectivity∗
"... In this work we consider temporal networks, the links of which are available only at random times (randomly available temporal networks). Our networks are ephemeral: their links appear sporadically, only at certain times, within a given maximum time (lifetime of the net). More specifically, our tem ..."
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Cited by 5 (0 self)
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In this work we consider temporal networks, the links of which are available only at random times (randomly available temporal networks). Our networks are ephemeral: their links appear sporadically, only at certain times, within a given maximum time (lifetime of the net). More specifically, our temporal networks notion concerns networks, whose edges (arcs) are assigned one or more random discretetime labels drawn from a set of natural numbers. The labels of an edge indicate the discrete moments in time at which the edge is available. In such networks, information (e.g., messages) have to follow temporal paths, i.e., paths, the edges of which are assigned a strictly increasing sequence of labels. We first examine a very hostile network: a clique, each edge of which is known to be available only
Merging costs for the additive MarcusLushnikov process, and UnionFind algorithms
"... Abstract. Starting with a monodisperse configuration with n size–1 particles, an additive Marcus–Lushnikov process evolves until it reaches its final state (a unique particle with mass n). At each of the n − 1 steps of its evolution, a merging cost is incurred, that depends on the sizes of the two p ..."
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Abstract. Starting with a monodisperse configuration with n size–1 particles, an additive Marcus–Lushnikov process evolves until it reaches its final state (a unique particle with mass n). At each of the n − 1 steps of its evolution, a merging cost is incurred, that depends on the sizes of the two particles involved, and on an independent random factor. This paper studies the asymptotic behaviour of the cumulated costs up to the kth clustering, under various regimes for (n, k), with applications to the study of Union–Find algorithms.
Ephemeral Networks with Random Availability of Links: The case of fast networksI
"... We consider here a model of temporal networks, the links of which are available only at certain moments in time, chosen randomly from a subset of the positive integers. We define the notion of the Temporal Diameter of such networks. We also define fast and slow such temporal networks with respect t ..."
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We consider here a model of temporal networks, the links of which are available only at certain moments in time, chosen randomly from a subset of the positive integers. We define the notion of the Temporal Diameter of such networks. We also define fast and slow such temporal networks with respect to the expected value of their temporal diameter. We then provide a partial characterisation of fast random temporal networks. We also define the critical availability as a measure of periodic random availability of the links of a network, required to make the network fast. We finally give a lower bound as well as an upper bound on the (critical) availability.
HACHAGE, ARBRES, CHEMINS & GRAPHES
"... Mathématiques discrètes et continues se rencontrent et se complètent volontiers harmonieusement. C’est cette thèse que nous voudrions illustrer en discutant un problème classique aux ramifications nombreuses—l’analyse du hachage avec essais linéaires. L’exemple est issu de l’analyse d’algorithmes, d ..."
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Mathématiques discrètes et continues se rencontrent et se complètent volontiers harmonieusement. C’est cette thèse que nous voudrions illustrer en discutant un problème classique aux ramifications nombreuses—l’analyse du hachage avec essais linéaires. L’exemple est issu de l’analyse d’algorithmes, domaine fondé par Knuth et qui se situe luimême “à cheval ” entre l’informatique, l’analyse combinatoire, et la théorie des probabilités. Lors de son traitement se croisent au fil du temps des approches très diverses, et l’on rencontrera des questions posées par Ramanujan à Hardy en 1913, un travail d’été de Knuth datant de 1962 et qui est à l’origine de l’analyse d’algorithmes en informatique, des recherches en analyse combinatoire du statisticien Kreweras, diverses rencontres avec les modèles de graphes aléatoires au sens d’Erdös et Rényi, un peu d’analyse complexe et d’analyse asymptotique, des arbres qu’on peut voir comme issus de processus de GaltonWatson particuliers, et, pour finir, un peu de processus, dont l’ineffable mouvement Brownien! Tout ceci contribuant in fine à une compréhension très précise d’un modèle simple d’aléa discret.