Two applications of information complexity
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
An improved data stream algorithm for frequency moments
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal space lower bounds for all frequency moments
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal approximations of the frequency moments of data streams
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Multi-pass geometric algorithms
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Buffering in query evaluation over XML streams
Proceedings of the twenty-fourth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Streaming and sublinear approximation of entropy and information distances
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
The space complexity of pass-efficient algorithms for clustering
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Data streams: algorithms and applications
Foundations and Trends® in Theoretical Computer Science
A characterization of average case communication complexity
Information Processing Letters
Estimating Hybrid Frequency Moments of Data Streams
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
Optimal sampling from sliding windows
Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
A Note on Estimating Hybrid Frequency Moment of Data Streams
AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
A direct sum theorem in communication complexity via message compression
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Coresets and sketches for high dimensional subspace approximation problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
1-pass relative-error Lp-sampling with applications
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
On the exact space complexity of sketching and streaming small norms
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Choosing, agreeing, and eliminating in communication complexity
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
An Optimal Randomized Cell Probe Lower Bound for Approximate Nearest Neighbor Searching
SIAM Journal on Computing
Multiparty equality function computation in networks with point-to-point links
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
Optimal sampling from sliding windows
Journal of Computer and System Sciences
Finding longest increasing and common subsequences in streaming data
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Estimating hybrid frequency moments of data streams
Journal of Combinatorial Optimization
Streaming algorithms measured in terms of the computed quantity
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Choosing, Agreeing, and Eliminating in Communication Complexity
Computational Complexity
| Hi-index | 0.00 |
We present a new method for proving strong lower bounds in communication complexity. This method is based on the notion of the conditional information complexity of a function which is the minimum amount of information about the inputs that has to be revealed by a communication protocol for the function. While conditional information complexity is a lower bound on the communication complexity, we show that it also admits a direct sum theorem. Direct sum decomposition reduces our task to that of proving (conditional) information complexity lower bounds for simple problems (such as the AND of two bits). For the latter, wedevelop novel techniques based on Hellinger distance and its generalizations.Our paradigm leads to two main results:(1) An improved lower bound for the multi-party set-disjointness problem in the general communication complexity model, and a nearly optimal lower bound in the one-way communication model. As a consequence, we show that for any real k 2, approximating the k-th frequency moment in the data stream model requires \Omega (n^{1 - {2 \mathord{\left/ {\vphantom {2 k}} \right. \kern-\nulldelimiterspace} k}}) space; this resolves a conjecture of Alon, Matias, and Szegedy [3].(2) A lower bound for the Lp approximation problem in the general communication model; this solves an open problem of Saks and Sun [23]. As a consequence, we show that for p 2, approximating the Lp norm to within a factor of n^\varepsilon in the data stream model with constant number of passes requires \Omega (n^{1 - 4\varepsilon- {2 \mathord{\left/ {\vphantom {2 p}} \right. \kern-\nulldelimiterspace} p}}) space.