In the Maximum Cut with Limited Unbalance problem, we want to partition the vertices of a weighted graph into two sets of sizes differing at most by a given threshold B, so that the sum of the weights of the crossing ...
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In the Maximum Cut with Limited Unbalance problem, we want to partition the vertices of a weighted graph into two sets of sizes differing at most by a given threshold B, so that the sum of the weights of the crossing edges is maximum. This problem has been introduced in (Galbiati and Maffioli, Theor Comput Sci 385 (2007), 78-87) where polynomial time randomized approximation algorithms are proposed and their performance guarantees are analyzed in the case of non-negative integer weights. In this article, we present extensive computational experience with these algorithms on a large number of different graphs. We then extend the analysis of these algorithms to integer weights not restricted in sign, and continue the computational testing. It turns out that the approximation ratios obtained are always substantially better than those guaranteed by the theoretical analysis. (C) 2010 Wiley Periodicals, Inc. NETWORKS, Vol. 55(3), 247-255 2010
We investigate the problem of estimating on the fly the frequency at which items recur in large scale distributed data streams, which has become the norm in cloud-based application. This paper presents CASE, a combina...
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ISBN:
(纸本)9781467377416
We investigate the problem of estimating on the fly the frequency at which items recur in large scale distributed data streams, which has become the norm in cloud-based application. This paper presents CASE, a combination of tools and probabilistic algorithms from the data streaming model. In this model, functions are estimated on a huge sequence of data items, in an online fashion, and with a very small amount of memory with respect to both the size of the input stream and the values domain from which data items are drawn. We derive upper and lower bounds on the quality of CASE, improving upon the Count-Min sketch algorithm which has, so far, been the best algorithm in terms of space and time performance to estimate the frequency of data items. We prove that CASE guarantees an (epsilon, delta)-approximation of the frequency of all the items, provided they are not rare, in a space-efficient way and for any input stream. Experiments on both synthetic and real datasets confirm our analysis.
Tensor decomposition methods are well-known tools for multilinear feature extraction from multi-way arrays with many important applications in signal processing and machine learning. Nonnegative Tensor Factorization (...
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ISBN:
(纸本)9781538669792
Tensor decomposition methods are well-known tools for multilinear feature extraction from multi-way arrays with many important applications in signal processing and machine learning. Nonnegative Tensor Factorization (NTF) is a particular case of such methods, mostly addressed for processing nonnegative multi-way arrays, such as hyperspectral observations or a set of images. One of the most efficient algorithms for NTF is the Hierarchical Alternating Least Squares (HALS) algorithm that belongs to a family of coordinate gradient descent updates. Despite its very good numerical properties, its computational complexity is quite large for large-scale datasets. In this study, we propose the randomized extension of the HALS, which considerably decreases its computational complexity with respect to the standard HALS. The numerical experiments, performed for various large-scale observations, confirm that the proposed algorithm is much faster than the standard one at the cost of slightly decreased performance.
Estimating the frequency of any piece of information in large-scale distributed data streams became of utmost importance in the last decade (e.g., in the context of network monitoring, big data, etc.). If some elegant...
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ISBN:
(纸本)9781509018499
Estimating the frequency of any piece of information in large-scale distributed data streams became of utmost importance in the last decade (e.g., in the context of network monitoring, big data, etc.). If some elegant solutions have been proposed recently, their approximation is computed from the inception of the stream. In a runtime distributed context, one would prefer to gather information only about the recent past. This may be led by the need to save resources or by the fact that recent information is more relevant. In this paper, we consider the sliding window model and propose two different (on-line) algorithms that approximate the items frequency in the active window. More precisely, we determine a (epsilon, delta)-additive-approximation meaning that the error is greater than epsilon only with probability delta. These solutions use a very small amount of memory with respect to the size N of the window and the number n of distinct items of the stream, namely, O(1/epsilon log 1/delta (log N + log n)) and O(1/tau epsilon log 1/delta (log N + log n)) bits of space, where tau is a parameter limiting memory usage. We also provide their distributed variant, i.e., considering the sliding window functional monitoring model. We compared the proposed algorithms to each other and also to the state of the art through extensive experiments on synthetic traces and real data sets that validate the robustness and accuracy of our algorithms.
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