In this paper we present a new approximation algorithm for the MAX ACYCLIC SUBGRAPH problem. Given an instance where the maximum acyclic subgraph contains (1/2 + delta) fraction of all edges, our algorithm finds an acyclic subgraph with (1/2 + Omega(delta/ log n)) fraction of all edges.

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The $2$-to-$2$ Games Theorem of [KMS-1, DKKMS-1, DKKMS-2, KMS-2] implies that it is NP-hard to distinguish between Unique Games instances with assignment satisfying at least $(\frac{1}{2}-\varepsilon)$ fraction of the constraints $vs.$ no assignment satisfying more than $\varepsilon$ fraction of the constraints, for every constant $\varepsilon>0$. We show that the reduction ... more >>>

An ordering constraint satisfaction problem (OCSP) is given by a positive integer $k$ and a constraint predicate $\Pi$ mapping permutations on $\{1,\ldots,k\}$ to $\{0,1\}$. Given an instance of OCSP$(\Pi)$ on $n$ variables and $m$ constraints, the goal is to find an ordering of the $n$ variables that maximizes the number ... more >>>