Related papers: QCSP on Reflexive Tournaments
We show that the maximum success probability of players sharing quantum entanglement in a two-player game with classical questions of logarithmic length and classical answers of constant length is NP-hard to approximate to within constant…
Given $k$ pairs of vertices $(s_i,t_i)$, $1\le i\le k$, of a digraph $G$, how can we test whether there exist $k$ vertex-disjoint directed paths from $s_i$ to $t_i$ for $1\le i\le k$? This is NP-complete in general digraphs, even for $k =…
Valued constraint satisfaction problems (VCSPs) constitute a large class of computational optimization problems. It was shown recently that, over finite domains, every VCSP is in P or NP-complete, depending on the admitted cost functions.…
Let \Gamma be a structure with a finite relational signature and a first-order definition in (R;*,+) with parameters from R, that is, a relational structure over the real numbers where all relations are semi-algebraic sets. In this article,…
This thesis investigates the extent to which the optimal value of a constraint satisfaction problem (CSP) can be approximated by some sentence of fixed point logic with counting (FPC). It is known that, assuming $\mathsf{P} \neq…
The constraint satisfaction problem (CSP) is a computational problem that includes a range of important problems in computer science. We point out that fundamental concepts of the CSP, such as the solution set of an instance and…
A notion of rigidity with respect to an arbitrary semidualizing complex C over a commutative noetherian ring R is introduced and studied. One of the main result characterizes C-rigid complexes. Specialized to the case when C is the relative…
We study constraint satisfaction problems (CSPs) in the presence of counting quantifiers $\exists^{\geq j}$, asserting the existence of $j$ distinct witnesses for the variable in question. As a continuation of our previous (CSR 2012) paper,…
Although the CSP (constraint satisfaction problem) is NP-complete, even in the case when all constraints are binary, certain classes of instances are tractable. We study classes of instances defined by excluding subproblems. This approach…
Satisfiability problems play a central role in computer science and engineering as a general framework for studying the complexity of various problems. Schaefer proved in 1978 that truth satisfaction of propositional formulas given a…
In a non-uniform Constraint Satisfaction problem CSP(G), where G is a set of relations on a finite set A, the goal is to find an assignment of values to variables subject to constraints imposed on specified sets of variables using the…
We show that the problem of deciding for a given finite relation algebra A whether the network satisfaction problem for A can be solved by the k-consistency procedure, for some natural number k, is undecidable. For the important class of…
An equivalent directed version of the celebrated unresolved conjecture of Erdos and Hajnal proposed by Alon, Pack, and Solymosi states that for every tournament H there exists epsilon(H)>0 such that every H-free n-vertex tournament T…
We define a $q$-linear path in a hypergraph $H$ as a sequence $(e_1,\ldots,e_L)$ of edges of $H$ such that $|e_i \cap e_{i+1}| \in [\![1,q]\!]$ and $e_i \cap e_j=\varnothing$ if $|i-j|>1$. In this paper, we study the connected components…
We prove that multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard. Our list here includes: determining the feasibility of a system of bilinear equations, deciding whether a 3-tensor…
Let $H$ be a 3-uniform hypergraph. A tournament $T$ defined on $V(T)=V(H)$ is a realization of $H$ if the edges of $H$ are exactly the 3-element subsets of $V(T)$ that induce 3-cycles. We characterize the 3-uniform hypergraphs that admit…
In pursuit of a deeper understanding of Boolean Promise Constraint Satisfaction Problems (PCSPs), we identify a class of problems with restricted structural complexity, which could serve as a promising candidate for complete…
Constraint satisfaction problems (CSPs) are ubiquitous in theoretical computer science. We study the problem of StrongCSPs, i.e. instances where a large induced sub-instance has a satisfying assignment. More formally, given a CSP instance…
A quadratically constrained quadratic program (QCQP) is an optimization problem in which the objective function is a quadratic function and the feasible region is defined by quadratic constraints. Solving non-convex QCQP to global…
A $k$-tournament $H$ on $n$ vertices is a pair $(V, A)$ for $2\leq k\leq n$, where $V(H)$ is a set of vertices, and $A(H)$ is a set of all possible $k$-tuples of vertices, such that for any $k$-subset $S$ of $V$, $A(H)$ contains exactly one…