Monotone circuits for connectivity require super-logarithmic depth
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
On data structures and asymmetric communication complexity
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Communication complexity
Quantum vs. classical communication and computation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Exponential separation of quantum and classical communication complexity
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
The quantum query complexity of approximating the median and related statistics
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On the Distributional Complexity of Disjontness
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
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
Lower bounds in communication complexity based on factorization norms
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
A near-optimal algorithm for computing the entropy of a stream
SODA '07 Proceedings of the eighteenth 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
The pattern matrix method for lower bounds on quantum communication
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
The average-case complexity of counting distinct elements
Proceedings of the 12th International Conference on Database Theory
Functional Monitoring without Monotonicity
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
A Multi-Round Communication Lower Bound for Gap Hamming and Some Consequences
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
A strong direct product theorem for disjointness
Proceedings of the forty-second ACM symposium on Theory of computing
An optimal algorithm for the distinct elements problem
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
The Partition Bound for Classical Communication Complexity and Query Complexity
CCC '10 Proceedings of the 2010 IEEE 25th Annual Conference on Computational Complexity
Better gap-hamming lower bounds via better round elimination
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Quantum one-way communication can be exponentially stronger than classical communication
Proceedings of the forty-third annual ACM symposium on Theory of computing
The complexity of data aggregation in directed networks
DISC'11 Proceedings of the 25th international conference on Distributed computing
The Value of Multiple Read/Write Streams for Approximating Frequency Moments
ACM Transactions on Computation Theory (TOCT)
Interactive information complexity
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Tight bounds for distributed functional monitoring
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
The cost of fault tolerance in multi-party communication complexity
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
From information to exact communication
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Understanding RFID counting protocols
Proceedings of the 19th annual international conference on Mobile computing & networking
Arthur-Merlin streaming complexity
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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We prove an optimal Ω(n) lower bound on the randomized communication complexity of the much-studied Gap-Hamming-Distance problem. As a consequence, we obtain essentially optimal multi-pass space lower bounds in the data stream model for a number of fundamental problems, including the estimation of frequency moments. The Gap-Hamming-Distance problem is a communication problem, wherein Alice and Bob receive n-bit strings x and y, respectively. They are promised that the Hamming distance between x and y is either at least n/2+√n or at most n/2-√n, and their goal is to decide which of these is the case. Since the formal presentation of the problem by Indyk and Woodruff (FOCS, 2003), it had been conjectured that the naive protocol, which uses n bits of communication, is asymptotically optimal. The conjecture was shown to be true in several special cases, e.g., when the communication is deterministic, or when the number of rounds of communication is limited. The proof of our aforementioned result, which settles this conjecture fully, is based on a new geometric statement regarding correlations in Gaussian space, related to a result of C. Borell (1985). To prove this geometric statement, we show that random projections of not-too-small sets in Gaussian space are close to a mixture of translated normal variables.