Private vs. common random bits in communication complexity
Information Processing Letters
The space complexity of approximating the frequency moments
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Next century challenges: scalable coordination in sensor networks
MobiCom '99 Proceedings of the 5th annual ACM/IEEE international conference on Mobile computing and networking
Data streams: algorithms and applications
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the 2003 ACM SIGMOD international conference on Management of data
ICDE '06 Proceedings of the 22nd International Conference on Data Engineering
Estimating entropy over data streams
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
A geometric approach to monitoring threshold functions over distributed data streams
ACM Transactions on Database Systems (TODS)
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
Efficient and private distance approximation in the communication and streaming models
Efficient and private distance approximation in the communication and streaming models
Sketching and Streaming Entropy via Approximation Theory
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Multi-dimensional online tracking
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Algorithms for distributed functional monitoring
ACM Transactions on Algorithms (TALG)
An optimal lower bound on the communication complexity of gap-hamming-distance
Proceedings of the forty-third annual ACM symposium on Theory of computing
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
Continuous sampling from distributed streams
Journal of the ACM (JACM)
Randomized algorithms for tracking distributed count, frequencies, and ranks
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Continuous distributed counting for non-monotonic streams
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Tight bounds for distributed functional monitoring
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Tracking distributed aggregates over time-based sliding windows
SSDBM'12 Proceedings of the 24th international conference on Scientific and Statistical Database Management
The continuous distributed monitoring model
ACM SIGMOD Record
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The notion of distributed functional monitoring was recently introduced by Cormode, Muthukrishnan and Yi to initiate a formal study of the communication cost of certain fundamental problems arising in distributed systems, especially sensor networks. In this model, each of k sites reads a stream of tokens and is in communication with a central coordinator, who wishes to continuously monitor some function f of *** , the union of the k streams. The goal is to minimize the number of bits communicated by a protocol that correctly monitors f (*** ), to within some small error. As in previous work, we focus on a threshold version of the problem, where the coordinator's task is simply to maintain a single output bit, which is 0 whenever f (*** ) ≤ *** (1 *** *** ) and 1 whenever f (*** ) *** *** . Following Cormode et al., we term this the (k ,f ,*** ,*** ) functional monitoring problem. In previous work, some upper and lower bounds were obtained for this problem, with f being a frequency moment function, e.g., F 0 , F 1 , F 2 . Importantly, these functions are monotone . Here, we further advance the study of such problems, proving three new classes of results. First, we provide nontrivial monitoring protocols when f is either H , the empirical Shannon entropy of a stream, or any of a related class of entropy functions (Tsallis entropies). These are the first nontrivial algorithms for distributed monitoring of non-monotone functions. Second, we study the effect of non-monotonicity of f on our ability to give nontrivial monitoring protocols, by considering f = F p with deletions allowed, as well as f = H . Third, we prove new lower bounds on this problem when f = F p , for several values of p .