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
Adaptive filters for continuous queries over distributed data streams
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
Distributed set-expression cardinality estimation
VLDB '04 Proceedings of the Thirtieth international conference on Very large data bases - Volume 30
Algorithms for distributed functional monitoring
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Probabilistic computations: Toward a unified measure of complexity
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Multi-dimensional online tracking
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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
Randomized algorithms for tracking distributed count, frequencies, and ranks
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Prediction-based geometric monitoring over distributed data streams
SIGMOD '12 Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data
Tight bounds for distributed functional monitoring
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Event processing of monitoring data of large hi-tech manufacturing equipment: DEBS grand challenge
Proceedings of the 6th ACM International Conference on Distributed Event-Based Systems
How robust are linear sketches to adaptive inputs?
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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Consider the following problem: We have k players each receiving a stream of items, and communicating with a central coordinator. Let the multiset of items received by player i up until time t be Ai(t). The coordinator's task is to monitor a given function f computed over the union of the inputs ∪i Ai(t), continuously at all times t. The goal is to minimize the number of bits communicated between the players and the coordinator. Of interest is the approximate version where the coordinator outputs 1 if f ≥ τ and 0 if f≤ (1−&epsis;)τ. This defines the (k,f,τ,&epsis;) 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 the well-studied streaming model and communication complexity. Yet few formal bounds are known for functional monitoring. We give upper and lower bounds for the (k,f,τ,&epsis;) problem for some of the basic f's. In particular, we study the frequency moments Fp for p=0,1,2. For F0 and F1, we obtain monitoring algorithms with cost almost the same as algorithms that compute the function for a single instance of time. However, for F2 the monitoring problem seems to be much harder than computing the function for a single time instance. We give a carefully constructed multiround algorithm that uses “sketch summaries” at multiple levels of details and solves the (k,F2,τ,&epsis;) problem with communication Õ(k2/&epsis; + k3/2/&epsis;3). Our algorithmic techniques are likely to be useful for other functional monitoring problems as well.