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56
What’s Hot and What’s Not: Tracking Most Frequent Items Dynamically
, 2003
"... Most database management systems maintain statistics on the underlying relation. One of the important statistics is that of the “hot items” in the relation: those that appear many times (most frequently, or more than some threshold). For example, endbiased histograms keep the hot items as part of t ..."
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Cited by 201 (13 self)
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Most database management systems maintain statistics on the underlying relation. One of the important statistics is that of the “hot items” in the relation: those that appear many times (most frequently, or more than some threshold). For example, endbiased histograms keep the hot items as part of the histogram and are used in selectivity estimation. Hot items are used as simple outliers in data mining, and in anomaly detection in networking applications. We present a new algorithm for dynamically determining the hot items at any time in the relation that is undergoing deletion operations as well as inserts. Our algorithm maintains a small space data structure that monitors the transactions on the relation, and when required, quickly outputs all hot items, without rescanning the relation in the database. With userspecified probability, it is able to report all hot items. Our algorithm relies on the idea of “group testing”, is simple to implement, and has provable quality, space and time guarantees. Previously known algorithms for this problem that make similar quality and performance guarantees can not handle deletions, and those that handle deletions can not make similar guarantees without rescanning the database. Our experiments with real and synthetic data shows that our algorithm is remarkably accurate in dynamically tracking the hot items independent of the rate of insertions and deletions.
Combinatorial Algorithms for Compressed Sensing
 In Proc. of SIROCCO
, 2006
"... Abstract — In sparse approximation theory, the fundamental problem is to reconstruct a signal A ∈ R n from linear measurements 〈A, ψi 〉 with respect to a dictionary of ψi’s. Recently, there is focus on the novel direction of Compressed Sensing [1] where the reconstruction can be done with very few—O ..."
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Cited by 117 (1 self)
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Abstract — In sparse approximation theory, the fundamental problem is to reconstruct a signal A ∈ R n from linear measurements 〈A, ψi 〉 with respect to a dictionary of ψi’s. Recently, there is focus on the novel direction of Compressed Sensing [1] where the reconstruction can be done with very few—O(k log n)— linear measurements over a modified dictionary if the signal is compressible, that is, its information is concentrated in k coefficients with the original dictionary. In particular, these results [1], [2], [3] prove that there exists a single O(k log n) × n measurement matrix such that any such signal can be reconstructed from these measurements, with error at most O(1) times the worst case error for the class of such signals. Compressed sensing has generated tremendous excitement both because of the sophisticated underlying Mathematics and because of its potential applications. In this paper, we address outstanding open problems in Compressed Sensing. Our main result is an explicit construction of a nonadaptive measurement matrix and the corresponding reconstruction algorithm so that with a number of measurements polynomial in k, log n, 1/ε, we can reconstruct compressible signals. This is the first known polynomial time explicit construction of any such measurement matrix. In addition, our result improves the error guarantee from O(1) to 1 + ε and improves the reconstruction time from poly(n) to poly(k log n). Our second result is a randomized construction of O(k polylog(n)) measurements that work for each signal with high probability and gives perinstance approximation guarantees rather than over the class of all signals. Previous work on Compressed Sensing does not provide such perinstance approximation guarantees; our result improves the best known number of measurements known from prior work in other areas including Learning Theory [4], [5], Streaming algorithms [6], [7], [8] and Complexity Theory [9] for this case. Our approach is combinatorial. In particular, we use two parallel sets of group tests, one to filter and the other to certify and estimate; the resulting algorithms are quite simple to implement. I.
What's New: Finding Significant Differences in Network Data Streams
 in Proc. of IEEE Infocom
, 2004
"... Monitoring and analyzing network traffic usage patterns is vital for managing IP Networks. An important problem is to provide network managers with information about changes in traffic, informing them about "what's new". Specifically, we focus on the challenge of finding significantly ..."
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Cited by 85 (8 self)
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Monitoring and analyzing network traffic usage patterns is vital for managing IP Networks. An important problem is to provide network managers with information about changes in traffic, informing them about "what's new". Specifically, we focus on the challenge of finding significantly large differences in traffic: over time, between interfaces and between routers. We introduce the idea of a deltoid: an item that has a large difference, whether the difference is absolute, relative or variational. We present novel...
Efficient tracing of failed nodes in sensor networks
 In Proceedings of the First ACM International Workshop on Wireless Sensor Networks and Applications
, 2002
"... This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author’s copyrig ..."
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Cited by 51 (0 self)
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This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author’s copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. Copyright c○2002 by the Association for Computing Machinery, Inc. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior
Defect Tolerance at the End of the Roadmap
 IN ITC
, 2004
"... Defect tolerance will become more important as feature sizes shrink closer to single digit nanometer dimensions. This is true whether the chips are manufactured using topdown methods (e.g., photolithography) or bottomup methods (e.g., chemically assembled electronic nanotechnology, or CAEN). In thi ..."
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Cited by 33 (1 self)
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Defect tolerance will become more important as feature sizes shrink closer to single digit nanometer dimensions. This is true whether the chips are manufactured using topdown methods (e.g., photolithography) or bottomup methods (e.g., chemically assembled electronic nanotechnology, or CAEN). In this paper, we propose a defect tolerance methodology centered around reconfigurable devices, a scalable testing method, and dynamic placeandroute. Our methodology is particularly well suited for CAEN.
Towards an algorithmic theory of compressed sensing
, 2005
"... In Approximation Theory, the fundamental problem is to reconstruct a signal A ∈ Rn from linear measurements 〈A, ψi 〉 with respect to a dictionary Ψ for Rn. Recently, there has been tremendous excitement about the novel direction of Compressed Sensing [10] where the reconstruction can be done with ve ..."
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Cited by 27 (1 self)
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In Approximation Theory, the fundamental problem is to reconstruct a signal A ∈ Rn from linear measurements 〈A, ψi 〉 with respect to a dictionary Ψ for Rn. Recently, there has been tremendous excitement about the novel direction of Compressed Sensing [10] where the reconstruction can be done with very few — Õ(k)—linear measurements over a modified dictionary Ψ ′ if the information of the signal is concentrated in k coefficients over an orthonormal basis Ψ. These results have reconstruction error on any given signal that is optimal with respect to a broad class of signals. In a series of papers and meetings over the past year, a theory of Compressed Sensing has been developed by mathematicians. We develop an algorithmic perspective for the Compressed Sensing problem, showing that Compressed Sensing results resonate with prior work in Group Testing, Learning theory and Streaming algorithms. Our main contributions are new algorithms that present the most general results for Compressed Sensing with 1 + ɛ approximation on every signal, faster The dictionary Ψ denotes an orthonormal basis for Rn, i.e. Ψ is a set of n realvalued vectors
Finding Popular Categories for RFID Tags
, 2008
"... As RFID tags are increasingly attached to everyday items, it quickly becomes impractical to collect data from every tag in order to extract useful information. In this paper, we consider the problem of identifying popular categories of RFID tags out of a large collection of tags, without reading all ..."
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Cited by 22 (9 self)
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As RFID tags are increasingly attached to everyday items, it quickly becomes impractical to collect data from every tag in order to extract useful information. In this paper, we consider the problem of identifying popular categories of RFID tags out of a large collection of tags, without reading all the tag data. We propose two algorithms based on the idea of group testing, which allows us to efficiently derive popular categories of tags. We evaluate our solutions using both theoretical analysis and simulation.
DESIGNING COMPRESSIVE SENSING DNA MICROARRAYS
"... A Compressive Sensing Microarray (CSM) is a new device for DNAbased identification of target organisms that leverages the nascent theory of Compressive Sensing (CS). In contrast to a conventional DNA microarray, in which each genetic sensor spot is designed to respond to a single target organism, i ..."
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Cited by 22 (4 self)
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A Compressive Sensing Microarray (CSM) is a new device for DNAbased identification of target organisms that leverages the nascent theory of Compressive Sensing (CS). In contrast to a conventional DNA microarray, in which each genetic sensor spot is designed to respond to a single target organism, in a CSM each sensor spot responds to a group of targets. As a result, significantly fewer total sensor spots are required. In this paper, we study how to design group identifier probes that simultaneously account for both the constraints from the CS theory and the biochemistry of probetarget DNA hybridization. We employ Belief Propagation as a CS recovery method to estimate target concentrations from the microarray intensities.
Combinatorial search on graphs motivated by bioinformatics applications: A brief survey
 WG 2005. LNCS
, 2005
"... Abstract. The goal of this paper is to present a brief survey of a collection of methods and results from the area of combinatorial search [1,8] focusing on graph reconstruction using queries of different type. The study is motivated by applications to genome sequencing. ..."
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Cited by 18 (0 self)
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Abstract. The goal of this paper is to present a brief survey of a collection of methods and results from the area of combinatorial search [1,8] focusing on graph reconstruction using queries of different type. The study is motivated by applications to genome sequencing.
GraphConstrained Group Testing
, 2010
"... Nonadaptive group testing involves grouping arbitrary subsets of n items into different pools. Each pool is then tested and defective items are identified. A fundamental question involves minimizing the number of pools required to identify at most d defective items. Motivated by applications in net ..."
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Cited by 17 (2 self)
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Nonadaptive group testing involves grouping arbitrary subsets of n items into different pools. Each pool is then tested and defective items are identified. A fundamental question involves minimizing the number of pools required to identify at most d defective items. Motivated by applications in network tomography, sensor networks and infection propagation we formulate group testing problems on graphs. Unlike conventional group testing problems each group here must conform to the constraints imposed by a graph. For instance, items can be associated with vertices and each pool is any set of nodes that must be path connected. In this paper we associate a test with a random walk. In this context conventional group testing corresponds to the special case of a complete graph on n vertices. For interesting classes of graphs we arrive at a rather surprising result, namely, that the number of tests required to identify d defective items is substantially similar to that required in conventional group testing problems, where no such constraints on pooling is imposed. Specifically, if T (n) corresponds to the mixing time of the graph G, we show that with m = O(d 2 T 2 (n) log(n/d)) nonadaptive tests, one can identify the defective items. Consequently, for the ErdősRényi random graph G(n, p), as well as expander graphs with constant spectral gap, it follows that m = O(d 2 log 3 n) nonadaptive tests