We show that in the bounded degree model for graph property testing,
adaptivity is essential. An algorithm is *non-adaptive* if it makes all queries to the input before receiving any answers. We call a property *non-trivial* if it does not depend only on the degree distribution of the nodes. We ... more >>>

We show that, assuming the Unique Games Conjecture, it is NP-hard to approximate Max 2-Sat within $\alpha_{LLZ}^{-}+\epsilon$, where $0.9401 < \alpha_{LLZ}^{-} < 0.9402$ is the believed approximation ratio of the algorithm of Lewin, Livnat and Zwick.

This result is surprising considering the fact that balanced instances of Max 2-Sat, i.e. ... more >>>

We give a tight lower bound of Omega(\sqrt{n}) for the randomized one-way communication complexity of the Boolean Hidden Matching Problem [BJK04]. Since there is a quantum one-way communication complexity protocol of O(log n) qubits for this problem, we obtain an exponential separation of quantum and classical one-way communication complexity for ... more >>>