Gábor Kun, Mario Szegedy

The well known dichotomy conjecture of Feder and

Vardi states that for every ﬁnite family Γ of constraints CSP(Γ) is

either polynomially solvable or NP-hard. Bulatov and Jeavons re-

formulated this conjecture in terms of the properties of the algebra

P ol(Γ), where the latter is ...
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Per Austrin, Venkatesan Guruswami, Johan Håstad

We prove the following hardness result for a natural promise variant of the classical CNF-satisfiability problem: Given a CNF-formula where each clause has width $w$ and the guarantee that there exists an assignment satisfying at least $g = \lceil \frac{w}{2}\rceil -1$ literals in each clause, it is NP-hard to find ... more >>>

Joshua Brakensiek, Venkatesan Guruswami

Finding a proper coloring of a $t$-colorable graph $G$ with $t$ colors is a classic NP-hard problem when $t\ge 3$. In this work, we investigate the approximate coloring problem in which the objective is to find a proper $c$-coloring of $G$ where $c \ge t$. We show that for all ... more >>>

Joshua Brakensiek, Venkatesan Guruswami

Promise CSPs are a relaxation of constraint satisfaction problems where the goal is to find an assignment satisfying a relaxed version of the constraints. Several well known problems can be cast as promise CSPs including approximate graph and hypergraph coloring, discrepancy minimization, and interesting variants of satisfiability. Similar to CSPs, ... more >>>

Joshua Brakensiek, Venkatesan Guruswami, Marcin Wrochna, Stanislav Zivny

In the field of constraint satisfaction problems (CSP), promise CSPs are an exciting new direction of study. In a promise CSP, each constraint comes in two forms: "strict" and "weak," and in the associated decision problem one must distinguish between being able to satisfy all the strict constraints versus not ... more >>>