Andrei Bulatov

The Constraint Satisfaction Problem (CSP) provides a common framework for many combinatorial problems. The general CSP is known to be NP-complete; however, certain restrictions on a possible form of constraints may affect the complexity, and lead to tractable problem classes. There is, therefore, a fundamental research direction, aiming to separate ... more >>>

Andrei Bulatov

A wide variety of combinatorial problems can be represented in the form of the Constraint Satisfaction Problem (CSP). The general CSR is known to be NP-complete, however, some restrictions on the possible form of constraints may lead to a tractable subclass. Jeavons and coauthors have shown that the complexity of ... more >>>

Charanjit Jutla

Venkatesan Guruswami, Kunal Talwar

We prove a strong inapproximability result for routing on directed

graphs with low congestion. Given as input a directed graph on $N$

vertices and a set of source-destination pairs that can be connected

via edge-disjoint paths, we prove that it is hard, assuming NP

doesn't have $n^{O(\log\log n)}$ time randomized ...
more >>>

Andrei A. Bulatov

The Counting Constraint Satisfaction Problem (#CSP(H)) over a finite

relational structure H can be expressed as follows: given a

relational structure G over the same vocabulary,

determine the number of homomorphisms from G to H.

In this paper we characterize relational structures H for which

#CSP(H) can be solved in ...
more >>>

Libor Barto, Marcin Kozik

An algorithm for a constraint satisfaction problem is called robust if it outputs an assignment satisfying at least $(1-g(\varepsilon))$-fraction of the constraints given a $(1-\varepsilon)$-satisfiable instance, where $g(\varepsilon) \rightarrow 0$ as $\varepsilon \rightarrow 0$, $g(0)=0$.

Guruswami and Zhou conjectured a characterization of constraint languages for which the corresponding constraint satisfaction ...
more >>>

Venkatesan Guruswami, Euiwoong Lee

We study two natural extensions of Constraint Satisfaction Problems (CSPs). {\em Balance}-Max-CSP requires that in any feasible assignment each element in the domain is used an equal number of times. An instance of {\em Hard}-Max-CSP consists of {\em soft constraints} and {\em hard constraints}, and the goal is to maximize ... more >>>

Sanjana Kolisetty, Linh Le, Ilya Volkovich, Mihalis Yannakakis

A graph $G$ has an \emph{$S$-factor} if there exists a spanning subgraph $F$ of $G$ such that for all $v \in V: \deg_F(v) \in S$.

The simplest example of such factor is a $1$-factor, which corresponds to a perfect matching in a graph. In this paper we study the computational ...
more >>>