Related papers: Making the long code shorter, with applications to…
Recent advancements in algorithms for sequential decision-making under imperfect information have shown remarkable success in large games such as limit- and no-limit poker. These algorithms traditionally formalize the games using the…
We present a novel algorithm that solves the turbo code LP decoding problem in a fininte number of steps by Euclidean distance minimizations, which in turn rely on repeated shortest path computations in the trellis graph representing the…
We consider the problem of testing small set expansion for general graphs. A graph $G$ is a $(k,\phi)$-expander if every subset of volume at most $k$ has conductance at least $\phi$. Small set expansion has recently received significant…
We devise an algorithm that approximately computes the number of paths of length $k$ in a given directed graph with $n$ vertices up to a multiplicative error of $1 \pm \varepsilon$. Our algorithm runs in time $\varepsilon^{-2} 4^k(n+m)…
Admissibility has been studied for games of infinite duration with Boolean objectives. We extend here this study to games of infinite duration with quantitative objectives. First, we show that, un- der the assumption that optimal worst-case…
We provide a unifying, black-box tool for establishing existence of approximate equilibria in weighted congestion games and, at the same time, bounding their Price of Stability. Our framework can handle resources with general…
Motivated in part by hook-content formulas for certain restricted partitions in representation theory, we consider the total number of hooks of fixed length in odd versus distinct partitions. We show that there are more hooks of length $2$,…
We prove game-theoretic versions of several classical results on nonrepetitive sequences, showing the existence of winning strategies using an extension of the Lov\'asz Local Lemma which can dramatically reduce the number of edges needed in…
This paper initiates the study of a class of entangled games, mono-state games, denoted by $(G,\psi)$, where $G$ is a two-player one-round game and $\psi$ is a bipartite state independent of the game $G$. In the mono-state game $(G,\psi)$,…
We give an explicit (in particular, deterministic polynomial time) construction of subspaces X of R^N of dimension (1-o(1))N such that for every element x in X, |x|_1 and N^{1/2} |x|_2 are equivalent up to a factor of (log N)^{log log log…
A strong blocking set in a finite projective space is a set of points that intersects each hyperplane in a spanning set. We provide a new graph theoretic construction of such sets: combining constant-degree expanders with asymptotically…
The best algorithm for approximating Steiner tree has performance ratio $\ln(4)+\epsilon \approx 1.386$ [J. Byrka et al., \textit{Proceedings of the 42th Annual ACM Symposium on Theory of Computing (STOC)}, 2010, pp. 583-592], whereas the…
We show that given an explicit description of a multiplayer game, with a classical verifier and a constant number of players, it is QMA-hard, under randomized reductions, to distinguish between the cases when the players have a strategy…
In this work, we construct the first locally-correctable codes (LCCs), and locally-testable codes (LTCs) with constant rate, constant relative distance, and sub-polynomial query complexity. Specifically, we show that there exist binary LCCs…
The decoding error probability of codes is studied as a function of their block length. It is shown that the existence of codes with a polynomially small decoding error probability implies the existence of codes with an exponentially small…
We consider a game in which a cop searches for a moving robber on a connected graph using distance probes, which is a slight variation on one introduced by Seager. Carragher, Choi, Delcourt, Erickson and West showed that for any $n$-vertex…
Counting the independent sets of a graph is a classical #P-complete problem, even in the bipartite case. We give an exponential-time approximation scheme for this problem which is faster than the best known algorithm for the exact problem.…
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 $n^{\tilde \Omega(log n)}$…
We study the problem of finding optimal correlated equilibria of various sorts in extensive-form games: normal-form coarse correlated equilibrium (NFCCE), extensive-form coarse correlated equilibrium (EFCCE), and extensive-form correlated…
We consider the question of approximating Max 2-CSP where each variable appears in at most $d$ constraints (but with possibly arbitrarily large alphabet). There is a simple $(\frac{d+1}{2})$-approximation algorithm for the problem. We prove…