A Bloom filter is a simple data structure supporting membership queries on a set. The standard Bloom filter does not support the delete operation, therefore, many applications use a counting Bloom filter to enable deletion. This paper proposes a generalization of the counting Bloom filter approach, called "autoscaling Bloom filters", which allows adjustment of its capacity with probabilistic bounds on false positives and true positives. In essence, the autoscaling Bloom filter is a binarized counting Bloom filter with an adjustable binarization threshold. We present the mathematical analysis of the performance as well as give a procedure for minimization of the false positive rate.
A recent probabilistic analysis of the SBF is presented in @cite_10 . Detailed surveys on BFs and their applications are provided in @cite_13 and @cite_2 . Recent applications of BFs and their modifications include certificate revocation for smart grids @cite_14 . An important aspect for the applicability of BFs in modern networking applications is the processing speed of a filter. In order to improve the speed of the membership check, the authors in @cite_25 proposed a novel filter type called Ultra-Fast BFs. In @cite_6 it was shown that BFs can be accelerated (in terms of processing speed) by using particular types of hashing functions.
@cite_14 @cite_10 @cite_6 @cite_2 @cite_13 @cite_25
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The network link speed is increasing at an alarming rate, which requires all network functions on routers switches to keep pace. Bloom filter is a widely-used membership check data structure in network applications. It also faces the urgent demand of improving the performance in membership check speed. To this end, this paper proposes a new Bloom filter variant called Ultra-Fast Bloom Filters, by leveraging the SIMD techniques. We make three improvements for the UFBF to accelerate the membership check speed. First, we develop a novel hash computation algorithm which can compute multiple hash functions in parallel with the use of SIMD instructions. Second, we change a Bloom filter's bit-test process from sequential to parallel. Third, we increase the cache efficiency of membership check by encoding an element's information to a small block which can easily fit into a cache-line. Both theoretical analysis and extensive simulations show that the UFBF greatly exceeds the state-of-the-art Bloom filter variants on membership check speed. Standard Mel frequency cepstrum coefficient (MFCC) computation technique utilizes discrete cosine transform (DCT) for decorrelating log energies of filter bank output. The use of DCT is reasonable here as the covariance matrix of Mel filter bank log energy (MFLE) can be compared with that of highly correlated Markov-I process. This full-band based MFCC computation technique where each of the filter bank output has contribution to all coefficients, has two main disadvantages. First, the covariance matrix of the log energies does not exactly follow Markov-I property. Second, full-band based MFCC feature gets severely degraded when speech signal is corrupted with narrow-band channel noise, though few filter bank outputs may remain unaffected. In this work, we have studied a class of linear transformation techniques based on block wise transformation of MFLE which effectively decorrelate the filter bank log energies and also capture speech information in an efficient manner. A thorough study has been carried out on the block based transformation approach by investigating a new partitioning technique that highlights associated advantages. This article also reports a novel feature extraction scheme which captures complementary information to wide band information; that otherwise remains undetected by standard MFCC and proposed block transform (BT) techniques. The proposed features are evaluated on NIST SRE databases using Gaussian mixture model-universal background model (GMM-UBM) based speaker recognition system. We have obtained significant performance improvement over baseline features for both matched and mismatched condition, also for standard and narrow-band noises. The proposed method achieves significant performance improvement in presence of narrow-band noise when clubbed with missing feature theory based score computation scheme. Our growing reliance on online services accessible on the Internet demands highly available systems that provide correct service without interruptions. Software bugs, operator mistakes, and malicious attacks are a major cause of service interruptions and they can cause arbitrary behavior, that is, Byzantine faults. This article describes a new replication algorithm, BFT, that can be used to build highly available systems that tolerate Byzantine faults. BFT can be used in practice to implement real services: it performs well, it is safe in asynchronous environments such as the Internet, it incorporates mechanisms to defend against Byzantine-faulty clients, and it recovers replicas proactively. The recovery mechanism allows the algorithm to tolerate any number of faults over the lifetime of the system provided fewer than 1 3 of the replicas become faulty within a small window of vulnerability. BFT has been implemented as a generic program library with a simple interface. We used the library to implement the first Byzantine-fault-tolerant NFS file system, BFS. The BFT library and BFS perform well because the library incorporates several important optimizations, the most important of which is the use of symmetric cryptography to authenticate messages. The performance results show that BFS performs 2p faster to 24p slower than production implementations of the NFS protocol that are not replicated. This supports our claim that the BFT library can be used to build practical systems that tolerate Byzantine faults. In this work, we propose the construction of two-channel wavelet filter banks for analyzing functions defined on the vertices of any arbitrary finite weighted undirected graph. These graph based functions are referred to as graph-signals as we build a framework in which many concepts from the classical signal processing domain, such as Fourier decomposition, signal filtering and downsampling can be extended to graph domain. Especially, we observe a spectral folding phenomenon in bipartite graphs which occurs during downsampling of these graphs and produces aliasing in graph signals. This property of bipartite graphs, allows us to design critically sampled two-channel filter banks, and we propose quadrature mirror filters (referred to as graph-QMF) for bipartite graph which cancel aliasing and lead to perfect reconstruction. For arbitrary graphs we present a bipartite subgraph decomposition which produces an edge-disjoint collection of bipartite subgraphs. Graph-QMFs are then constructed on each bipartite subgraph leading to “multi-dimensional” separable wavelet filter banks on graphs. Our proposed filter banks are critically sampled and we state necessary and sufficient conditions for orthogonality, aliasing cancellation and perfect reconstruction. The filter banks are realized by Chebychev polynomial approximations.