The main motivation for studying linear data structures and circuits is the intuition that non-linear advice cannot help in computing a linear operator. Jukna and Schnitger formalized this as a conjecture which states that all circuits computing a linear operator can be ``linearized," with only a constant size blow-up. We ... more >>>

Unique Games Conjecture (UGC), proposed by [Khot02], lies in the center of many inapproximability results. At the heart of UGC lies approximability of MAX-CUT, which is a special instance of Unique Game.[KhotKMO04, MosselOO05] showed that assuming Unique Games Conjecture, it is NP-hard to distinguish between MAX-CUT instance that has a ... more >>>

We introduce a generalization of the standard framework for studying the difficulty of two-prover games. Specifically, we study the model where Alice and Bob are allowed to communicate (with information constraints) --- in contrast to the usual two-prover game where they are not allowed to communicate after receiving their respective ... more >>>

In the recent paper of~\cite{BR16}, the authors show that, for any constant $10^{-15} > \varepsilon > 0$ the communication complexity of $\varepsilon$-approximate Nash equilibria in $2$-player $n \times n$ games is $n^{\Omega(\varepsilon)}$, resolving the long open problem of whether or not there exists a polylogarithmic communication protocol. In this paper ... more >>>

We prove a near optimal round-communication tradeoff for the two-party quantum communication complexity of disjointness. For protocols with $r$ rounds, we prove a lower bound of $\tilde{\Omega}(n/r)$ on the communication required for computing disjointness of input size $n$, which is optimal up to logarithmic factors. The previous best lower bound ... more >>>

We show that, assuming the (deterministic) Exponential Time Hypothesis, distinguishing between a graph with an induced $k$-clique and a graph in which all $k$-subgraphs have density at most $1-\epsilon$, requires $n^{\tilde \Omega(log n)}$ time. Our result essentially matches the quasi-polynomial algorithms of Feige and Seltser [FS97] and Barman [Bar15] for ... more >>>

The celebrated PPAD hardness result for finding an exact Nash equilibrium in a two-player game
initiated a quest for finding \emph{approximate} Nash equilibria efficiently, and is one of the major open questions in algorithmic game theory.

We study the computational complexity of finding an $\eps$-approximate Nash equilibrium with good social ... more >>>