Probabilistic counting algorithms for data base applications
Journal of Computer and System Sciences
Results on communication complexity classes
Journal of Computer and System Sciences
Theoretical Computer Science - Special issue on complexity theory and the theory of algorithms as developed in the CIS
Communication complexity
On data structures and asymmetric communication complexity
Journal of Computer and System Sciences
The space complexity of approximating the frequency moments
Journal of Computer and System Sciences
External memory algorithms
Space-efficient online computation of quantile summaries
SIGMOD '01 Proceedings of the 2001 ACM SIGMOD international conference on Management of data
Interaction in quantum communication and the complexity of set disjointness
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
An Approximate L1-Difference Algorithm for Massive Data Streams
SIAM Journal on Computing
Counting Distinct Elements in a Data Stream
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Frequency Estimation of Internet Packet Streams with Limited Space
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Two applications of information complexity
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
On notions of information transfer in VLSI circuits
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Informational Complexity and the Direct Sum Problem for Simultaneous Message Complexity
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Tight Lower Bounds for the Distinct Elements Problem
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Optimal space lower bounds for all frequency moments
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
An information statistics approach to data stream and communication complexity
Journal of Computer and System Sciences - Special issue on FOCS 2002
Optimal approximations of the frequency moments of data streams
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Graph distances in the streaming model: the value of space
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Streaming and sublinear approximation of entropy and information distances
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximate quantiles and the order of the stream
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
A near-optimal algorithm for computing the entropy of a stream
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Tight lower bounds for selection in randomly ordered streams
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Sketching information divergences
COLT'07 Proceedings of the 20th annual conference on Learning theory
Lower bounds for quantile estimation in random-order and multi-pass streaming
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Sliding-window top-k queries on uncertain streams
Proceedings of the VLDB Endowment
Comparison-based time-space lower bounds for selection
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
The average-case complexity of counting distinct elements
Proceedings of the 12th International Conference on Database Theory
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Revisiting the Direct Sum Theorem and Space Lower Bounds in Random Order Streams
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Comparison-based time-space lower bounds for selection
ACM Transactions on Algorithms (TALG)
Proceedings of the forty-second ACM symposium on Theory of computing
Sliding-window top-k queries on uncertain streams
The VLDB Journal — The International Journal on Very Large Data Bases
Theoretical Computer Science
A truly dynamic data structure for top-k queries on uncertain data
SSDBM'11 Proceedings of the 23rd international conference on Scientific and statistical database management
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Tight bounds for distributed functional monitoring
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Statistical estimation with bounded memory
Statistics and Computing
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We study the communication complexity of evaluating functions when the input data is randomly allocated (according to some known distribution) amongst two or more players, possibly with information overlap. This naturally extends previously studied variable partition models such as the best-case and worst-case partition models [32,29]. We aim to understand whether the hardness of a communication problem holds for almost every allocation of the input, as opposed to holding for perhaps just a few atypical partitions. A key application is to the heavily studied data stream model. There is a strong connection between our communication lower bounds and lower bounds in the data stream model that are "robust" to the ordering of the data. That is, we prove lower bounds for when the order of the items in the stream is chosen not adversarially but rather uniformly (or near-uniformly) from the set of all permuations. This random-order data stream model has attracted recent interest, since lower bounds here give stronger evidence for the inherent hardness of streaming problems. Our results include the first random-partition communication lower bounds for problems including multi-party set disjointness and gap-Hamming-distance. Both are tight. We also extend and improve previous results [19,7] for a form of pointer jumping that is relevant to the problem of selection (in particular, median finding). Collectively, these results yield lower bounds for a variety of problems in the random-order data stream model, including estimating the number of distinct elements, approximating frequency moments, and quantile estimation.