Elements of information theory
Elements of information theory
The space complexity of approximating the frequency moments
Journal of Computer and System Sciences
Proceedings of the 10th international conference on Architectural support for programming languages and operating systems
Counting Distinct Elements in a Data Stream
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Proceedings of the 2003 ACM SIGMOD international conference on Management of data
Algorithms for dynamic geometric problems over data streams
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
TinyDB: an acquisitional query processing system for sensor networks
ACM Transactions on Database Systems (TODS) - Special Issue: SIGMOD/PODS 2003
Holistic aggregates in a networked world: distributed tracking of approximate quantiles
Proceedings of the 2005 ACM SIGMOD international conference on Management of data
Sketching streams through the net: distributed approximate query tracking
VLDB '05 Proceedings of the 31st international conference on Very large data bases
Simpler algorithm for estimating frequency moments of data streams
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
ICDE '06 Proceedings of the 22nd International Conference on Data Engineering
Communication-efficient distributed monitoring of thresholded counts
Proceedings of the 2006 ACM SIGMOD international conference on Management of data
A geometric approach to monitoring threshold functions over distributed data streams
Proceedings of the 2006 ACM SIGMOD international conference on Management of data
Data streams: algorithms and applications
Foundations and Trends® in Theoretical Computer Science
Distributed Functional Compression through Graph Coloring
DCC '07 Proceedings of the 2007 Data Compression Conference
Distributed set-expression cardinality estimation
VLDB '04 Proceedings of the Thirtieth international conference on Very large data bases - Volume 30
IEEE Transactions on Information Theory
Multi-dimensional online tracking
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Flooding-Assisted Threshold Assignment for Aggregate Monitoring in Sensor Networks
ICDCN '09 Proceedings of the 10th International Conference on Distributed Computing and Networking
Optimal tracking of distributed heavy hitters and quantiles
Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Functional Monitoring without Monotonicity
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Distributed threshold selection for aggregate threshold monitoring in sensor networks
CCNC'09 Proceedings of the 6th IEEE Conference on Consumer Communications and Networking Conference
Optimal sampling from distributed streams
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Algorithms for distributed functional monitoring
ACM Transactions on Algorithms (TALG)
Uncovering Global Icebergs in Distributed Streams: Results and Implications
Journal of Network and Systems Management
An efficient decentralized algorithm for the distributed trigger counting problem
ICDCN'11 Proceedings of the 12th international conference on Distributed computing and networking
Online tracking of the dominance relationship of distributed multi-dimensional data
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Theory of data stream computing: where to go
Proceedings of the thirtieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Tracking distributed aggregates over time-based sliding windows
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Continuous distributed monitoring: a short survey
Proceedings of the First International Workshop on Algorithms and Models for Distributed Event Processing
Optimal random sampling from distributed streams revisited
DISC'11 Proceedings of the 25th international conference on Distributed computing
Lower bounds for number-in-hand multiparty communication complexity, made easy
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Multidimensional online tracking
ACM Transactions on Algorithms (TALG)
Online function tracking with generalized penalties
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Continuous sampling from distributed streams
Journal of the ACM (JACM)
Continuous distributed counting for non-monotonic streams
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Survey: Streaming techniques and data aggregation in networks of tiny artefacts
Computer Science Review
Tracking distributed aggregates over time-based sliding windows
SSDBM'12 Proceedings of the 24th international conference on Scientific and Statistical Database Management
Optimizing notifications of subscription-based forecast queries
SSDBM'12 Proceedings of the 24th international conference on Scientific and Statistical Database Management
Efficient protocols for distributed classification and optimization
ALT'12 Proceedings of the 23rd international conference on Algorithmic Learning Theory
The continuous distributed monitoring model
ACM SIGMOD Record
Efficient and scalable monitoring and summarization of large probabilistic data
Proceedings of the 2013 Sigmod/PODS Ph.D. symposium on PhD symposium
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We study what we call functional monitoring problems. We have k players each tracking their inputs, say player i tracking a multiset Ai(t) up until time t, and communicating with a central coordinator. The coordinator's task is to monitor a given function f computed over the union of the inputs ∪iAi(t), continuously at all times t. The goal is to minimize the number of bits communicated between the players and the coordinator. A simple example is when f is the sum, and the coordinator is required to alert when the sum of a distributed set of values exceeds a given threshold τ. Of interest is the approximate version where the coordinator outputs 1 if f ≥ τ and 0 if f ≤ (1 - ε)τ. This defines the (k, f, τ, ε) distributed, functional monitoring problem. Functional monitoring problems are fundamental in distributed systems, in particular sensor networks, where we must minimize communication; they also connect to problems in communication complexity, communication theory, and signal processing. Yet few formal bounds are known for functional monitoring. We give upper and lower bounds for the (k, f, τ, ε) problem for some of the basic f's. In particular, we study frequency moments (F0, F1, F2). For F0 and F1, we obtain continuously monitoring algorithms with costs almost the same as their one-shot computation algorithms. However, for F2 the monitoring problem seems much harder. We give a carefully constructed multi-round algorithm that uses "sketch summaries" at multiple levels of detail and solves the (k, F2, τ, ε) problem with communication Õ(k2/ε+ (√k/ε)3). Since frequency moment estimation is central to other problems, our results have immediate applications to histograms, wavelet computations, and others. Our algorithmic techniques are likely to be useful for other functional monitoring problems as well.