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Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

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Reports tagged with CSP:
TR00-042 | 21st June 2000
Lars Engebretsen

Lower Bounds for non-Boolean Constraint Satisfaction

Revisions: 1

We show that the k-CSP problem over a finite Abelian group G
cannot be approximated within |G|^{k-O(sqrt{k})}-epsilon, for
any constant epsilon>0, unless P=NP. This lower bound matches
well with the best known upper bound, |G|^{k-1}, of Serna,
Trevisan and Xhafa. The proof uses a combination of PCP
techniques---most notably a ... more >>>

TR04-097 | 2nd November 2004
Víctor Dalmau

Malt'sev Constraints made Simple

We give in this paper a different and simpler proof of the tractability of Mal'tsev contraints.

more >>>

TR11-071 | 27th April 2011
Serge Gaspers, Stefan Szeider

The Parameterized Complexity of Local Consistency

Revisions: 1

We investigate the parameterized complexity of deciding whether a constraint network is $k$-consistent. We show that, parameterized by $k$, the problem is complete for the complexity class co-W[2]. As secondary parameters we consider the maximum domain size $d$ and the maximum number $\ell$ of constraints in which a variable occurs. ... more >>>

TR16-142 | 11th September 2016
Jason Li, Ryan O'Donnell

Bounding laconic proof systems by solving CSPs in parallel

Revisions: 1

We show that the basic semidefinite programming relaxation value of any constraint satisfaction problem can be computed in NC; that is, in parallel polylogarithmic time and polynomial work. As a complexity-theoretic consequence we get that MIP1$[k,c,s] \subseteq $ PSPACE provided $s/c \leq (.62-o(1))k/2^k$, resolving a question of Austrin, Håstad, and ... more >>>

TR19-092 | 9th July 2019
Venkatesan Guruswami, Jakub Opršal, Sai Sandeep

Revisiting Alphabet Reduction in Dinur's PCP

Dinur's celebrated proof of the PCP theorem alternates two main steps in several iterations: gap amplification to increase the soundness gap by a large constant factor (at the expense of much larger alphabet size), and a composition step that brings back the alphabet size to an absolute constant (at the ... more >>>

TR19-181 | 9th December 2019
Michal Koucky, Vojtech Rodl, Navid Talebanfard

A Separator Theorem for Hypergraphs and a CSP-SAT Algorithm

We show that for every $r \ge 2$ there exists $\epsilon_r > 0$ such that any $r$-uniform hypergraph on $m$ edges with bounded vertex degree has a set of at most $(\frac{1}{2} - \epsilon_r)m$ edges the removal of which breaks the hypergraph into connected components with at most $m/2$ edges. ... more >>>

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