Relations Between Communication Complexity, Linear Arrangements, and Computational Complexity
FST TCS '01 Proceedings of the 21st Conference on Foundations of Software Technology and Theoretical Computer Science
Limitations of Learning via Embeddings in Euclidean Half-Spaces
COLT '01/EuroCOLT '01 Proceedings of the 14th Annual Conference on Computational Learning Theory and and 5th European Conference on Computational Learning Theory
Ordinal embeddings of minimum relaxation: General properties, trees, and ultrametrics
ACM Transactions on Algorithms (TALG)
Computational Complexity
Ordinal Embedding: Approximation Algorithms and Dimensionality Reduction
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Learning complexity vs communication complexity
Combinatorics, Probability and Computing
Complexity Lower Bounds using Linear Algebra
Foundations and Trends® in Theoretical Computer Science
Unbounded-error classical and quantum communication complexity
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
SIAM Journal on Computing
COLT'05 Proceedings of the 18th annual conference on Learning Theory
Space lower bounds for low-stretch greedy embeddings
SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
The approximate rank of a matrix and its algorithmic applications: approximate rank
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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Let d = d(n) be the minimum d such that for every sequence of n subsets F1, F2, . . . , Fn of {1, 2, . . . , n} there exist n points P1, P2, . . . , Pn and n hyperplanes H1, H2 .... , Hn in Rd such that Pj lies in the positive side of Hi iff j ∈ Fi. Then n/32 ≤ d(n) ≤ (1/2 + 0(1)) ċ n. This implies that the probabilistic unbounded-error 2-way complexity of almost all the Boolean functions of 2p variables is between p-5 and p, thus solving a problem of Yao and another problem of Paturi and Simon. The proof of (1) combines some known geometric facts with certain probabilistic arguments and a theorem of Milnor from real algebraic geometry.