Elements of information theory
Elements of information theory
The probabilistic communication complexity of set intersection
SIAM Journal on Discrete Mathematics
On the distributional complexity of disjointness
Theoretical Computer Science
Communication complexity
Lower bounds on the multiparty communication complexity
Journal of Computer and System Sciences
Proceedings of the 2003 ACM SIGMOD international conference on Management of data
Practical methods for shape fitting and kinetic data structures using core sets
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Approximating extent measures of points
Journal of the ACM (JACM)
Efficient top-K query calculation in distributed networks
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
An information statistics approach to data stream and communication complexity
Journal of Computer and System Sciences - Special issue on FOCS 2002
Finding (Recently) Frequent Items in Distributed Data Streams
ICDE '05 Proceedings of the 21st International Conference on Data Engineering
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
KLEE: a framework for distributed top-k query algorithms
VLDB '05 Proceedings of the 31st international conference on Very large data bases
ICDE '06 Proceedings of the 22nd International Conference on Data Engineering
Finding global icebergs over distributed data sets
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
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
An integrated efficient solution for computing frequent and top-k elements in data streams
ACM Transactions on Database Systems (TODS)
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Algorithms for distributed functional monitoring
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Shape sensitive geometric monitoring
Proceedings of the twenty-seventh ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Probabilistic computations: Toward a unified measure of complexity
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
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
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
Faster core-set constructions and data-stream algorithms in fixed dimensions
Computational Geometry: Theory and Applications
How to compress interactive communication
Proceedings of the forty-second ACM symposium on Theory of computing
Towards polynomial lower bounds for dynamic problems
Proceedings of the forty-second ACM symposium on Theory of computing
Optimal sampling from distributed streams
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART 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
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In this paper we prove lower bounds on randomized multiparty communication complexity, both in the blackboard model (where each message is written on a blackboard for all players to see) and (mainly) in the message-passing model, where messages are sent player-to-player. We introduce a new technique for proving such bounds, called symmetrization, which is natural, intuitive, and often easy to use. For example, for the problem where each of k players gets a bit-vector of length n, and the goal is to compute the coordinate-wise XOR of these vectors, we prove a tight lower bounds of Ω(nk) in the blackboard model. For the same problem with AND instead of XOR, we prove a lower bounds of roughly Ω(nk) in the message-passing model (assuming k ≤ n/3200) and Ω(n log k) in the blackboard model. We also prove lower bounds for bit-wise majority, for a graphconnectivity problem, and for other problems; the technique seems applicable to a wide range of other problems as well. The obtained communication lower bounds imply new lower bounds in the functional monitoring model [11] (also called the distributed streaming model). All of our lower bounds allow randomized communication protocols with two-sided error. We also use the symmetrization technique to prove several direct-sum-like results for multiparty communication.