eng
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2017-02-21
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10.4230/DFU.Vol7.15301
article
DFU, Volume 7, The Constraint Satisfaction Problem: Complexity and Approximability, Complete Volume
Krokhin, Andrei
Zivny, Stanislav
DFU, Volume 7, The Constraint Satisfaction Problem: Complexity and Approximability, Complete Volume
https://drops.dagstuhl.de/storage/02dagstuhl-follow-ups/dfu-vol007/DFU.Vol7.15301/DFU.Vol7.15301.pdf
Nonnumerical Algorithms and Problems
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
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2017-02-21
7
0:i
0:xii
10.4230/DFU.Vol7.15301.i
article
Front Matter, Table of Contents, Preface, List of Authors
Krokhin, Andrei
Zivny, Stanislav
Front Matter, Table of Contents, Preface, List of Authors
https://drops.dagstuhl.de/storage/02dagstuhl-follow-ups/dfu-vol007/DFU.Vol7.15301.i/DFU.Vol7.15301.i.pdf
Front Matter
Table of Contents
Preface
List of Authors
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
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2017-02-21
7
1
44
10.4230/DFU.Vol7.15301.1
article
Polymorphisms, and How to Use Them
Barto, Libor
Krokhin, Andrei
Willard, Ross
This article describes the algebraic approach to Constraint Satisfaction Problem that led to many developments in both CSP and universal algebra. No prior knowledge of universal algebra is assumed.
https://drops.dagstuhl.de/storage/02dagstuhl-follow-ups/dfu-vol007/DFU.Vol7.15301.1/DFU.Vol7.15301.1.pdf
Constraint satisfaction
Complexity
Universal algebra
Polymorphism
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
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2017-02-21
7
45
77
10.4230/DFU.Vol7.15301.45
article
Absorption in Universal Algebra and CSP
Barto, Libor
Kozik, Marcin
The algebraic approach to Constraint Satisfaction Problem led to many developments in both CSP and universal algebra. The notion of absorption was successfully applied on both sides of the connection. This article introduces the concept of absorption, illustrates its use in a number of basic proofs and provides an overview of the most important results obtained by using it.
https://drops.dagstuhl.de/storage/02dagstuhl-follow-ups/dfu-vol007/DFU.Vol7.15301.45/DFU.Vol7.15301.45.pdf
Constraint satisfaction problem
Algebraic approach
Absorption
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
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2017-02-21
7
79
111
10.4230/DFU.Vol7.15301.79
article
Constraint Satisfaction Problems over Numeric Domains
Bodirsky, Manuel
Mamino, Marcello
We present a survey of complexity results for constraint satisfaction problems (CSPs) over the integers, the rationals, the reals, and the complex numbers. Examples of such problems are feasibility of linear programs, integer linear programming, the max-atoms problem, Hilbert's tenth problem, and many more. Our particular focus is to identify those CSPs that can be solved in polynomial time, and to distinguish them from CSPs that are NP-hard. A very helpful tool for obtaining complexity classifications in this context is the concept of a polymorphism from universal algebra.
https://drops.dagstuhl.de/storage/02dagstuhl-follow-ups/dfu-vol007/DFU.Vol7.15301.79/DFU.Vol7.15301.79.pdf
Constraint satisfaction problems
Numerical domains
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
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2017-02-21
7
113
135
10.4230/DFU.Vol7.15301.113
article
Hybrid Tractable Classes of Constraint Problems
Cooper, Martin C.
Zivny, Stanislav
We present a survey of complexity results for hybrid constraint satisfaction problems (CSPs) and valued constraint satisfaction problems (VCSPs). These are classes of (V)CSPs defined by restrictions that are not exclusively language-based or structure-based.
https://drops.dagstuhl.de/storage/02dagstuhl-follow-ups/dfu-vol007/DFU.Vol7.15301.113/DFU.Vol7.15301.113.pdf
Constraint satisfaction problems
Optimisation
Tractability
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
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2017-02-21
7
137
157
10.4230/DFU.Vol7.15301.137
article
Backdoor Sets for CSP
Gaspers, Serge
Ordyniak, Sebastian
Szeider, Stefan
A backdoor set of a CSP instance is a set of variables whose instantiation moves the instance into a fixed class of tractable instances (an island of tractability). An interesting algorithmic task is to find a small backdoor set efficiently: once it is found we can solve the instance by solving a number of tractable instances. Parameterized complexity provides an adequate framework for studying and solving this algorithmic task, where the size of the backdoor set provides a natural parameter. In this survey we present some recent parameterized complexity results on CSP backdoor sets, focusing on backdoor sets into islands of tractability that are defined in terms of constraint languages.
https://drops.dagstuhl.de/storage/02dagstuhl-follow-ups/dfu-vol007/DFU.Vol7.15301.137/DFU.Vol7.15301.137.pdf
Backdoor sets
Constraint satisfaction problems
Parameterized complexity
Polymorphisms
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
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2017-02-21
7
159
177
10.4230/DFU.Vol7.15301.159
article
On the Complexity of Holant Problems
Guo, Heng
Lu, Pinyan
In this article we survey recent developments on the complexity of Holant problems. We discuss three different aspects of Holant problems: the decision version, exact counting, and approximate counting.
https://drops.dagstuhl.de/storage/02dagstuhl-follow-ups/dfu-vol007/DFU.Vol7.15301.159/DFU.Vol7.15301.159.pdf
Computational complexity
Counting complexity
Dichotomy theorems
Approximate counting
Holant problems
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
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2017-02-21
7
179
203
10.4230/DFU.Vol7.15301.179
article
Parameterized Constraint Satisfaction Problems: a Survey
Gutin, Gregory
Yeo, Anders
We consider constraint satisfaction problems parameterized above or below guaranteed values. One example is MaxSat parameterized above m/2: given a CNF formula F with m clauses, decide whether there is a truth assignment that satisfies at least m/2 + k clauses, where k is the parameter. Among other problems we deal with are MaxLin2-AA (given a system of linear equations over F_2 in which each equation has a positive integral weight, decide whether there is an assignment to the variables that satisfies equations of total weight at least W/2+k, where W is the total weight of all equations), Max-r-Lin2-AA (the same as MaxLin2-AA, but each equation has at most r variables, where r is a constant) and Max-r-Sat-AA (given a CNF formula F with m clauses in which each clause has at most r literals, decide whether there is a truth assignment satisfying at least sum_{i=1}^m (1-2^{r_i})+k clauses, where k is the parameter, r_i is the number of literals in clause i, and r is a constant). We also consider Max-r-CSP-AA, a natural generalization of both Max-r-Lin2-AA and Max-r-Sat-AA, order (or, permutation) constraint satisfaction problems parameterized above the average value and some other problems related to MaxSat. We discuss results, both polynomial kernels and parameterized algorithms, obtained for the problems mainly in the last few years as well as some open questions.
https://drops.dagstuhl.de/storage/02dagstuhl-follow-ups/dfu-vol007/DFU.Vol7.15301.179/DFU.Vol7.15301.179.pdf
Constraint satisfaction problems
Fixed-parameter tractability
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
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2017-02-21
7
205
231
10.4230/DFU.Vol7.15301.205
article
Counting Constraint Satisfaction Problems
Jerrum, Mark
This chapter surveys counting Constraint Satisfaction Problems (counting CSPs, or #CSPs) and their computational complexity. It aims to provide an introduction to the main concepts and techniques, and present a representative selection of results and open problems. It does not cover holants, which are the subject of a separate chapter.
https://drops.dagstuhl.de/storage/02dagstuhl-follow-ups/dfu-vol007/DFU.Vol7.15301.205/DFU.Vol7.15301.205.pdf
Approximation algorithms
Computational complexity
Constraint satisfaction problems
Counting problems
Partition functions
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
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1868-8977
2017-02-21
7
233
266
10.4230/DFU.Vol7.15301.233
article
The Complexity of Valued CSPs
Krokhin, Andrei
Zivny, Stanislav
We survey recent results on the broad family of problems that can be cast as valued constraint satisfaction problems (VCSPs). We discuss general methods for analysing the complexity of such problems, give examples of tractable cases, and identify general features of the complexity landscape.
https://drops.dagstuhl.de/storage/02dagstuhl-follow-ups/dfu-vol007/DFU.Vol7.15301.233/DFU.Vol7.15301.233.pdf
Constraint satisfaction problems
Optimisation
Tractability
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
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1868-8977
2017-02-21
7
267
285
10.4230/DFU.Vol7.15301.267
article
Algebra and the Complexity of Digraph CSPs: a Survey
Larose, Benoit
We present a brief survey of some of the key results on the interplay between algebraic and graph-theoretic methods in the study of the complexity of digraph-based constraint satisfaction problems.
https://drops.dagstuhl.de/storage/02dagstuhl-follow-ups/dfu-vol007/DFU.Vol7.15301.267/DFU.Vol7.15301.267.pdf
Constraint satisfaction problems
Polymorphisms
Digraphs
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
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2017-02-21
7
287
325
10.4230/DFU.Vol7.15301.287
article
Approximation Algorithms for CSPs
Makarychev, Konstantin
Makarychev, Yury
In this survey, we offer an overview of approximation algorithms for constraint satisfaction problems (CSPs) - we describe main results and discuss various techniques used for solving CSPs.
https://drops.dagstuhl.de/storage/02dagstuhl-follow-ups/dfu-vol007/DFU.Vol7.15301.287/DFU.Vol7.15301.287.pdf
Constraint satisfaction problems
Approximation algorithms
SDP
UGC
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
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1868-8977
2017-02-21
7
327
346
10.4230/DFU.Vol7.15301.327
article
Quantified Constraints in Twenty Seventeen
Martin, Barnaby
I present a survey of recent advances in the algorithmic and computational complexity theory of non-Boolean Quantified Constraint Satisfaction Problems, incorporating some more modern research directions.
https://drops.dagstuhl.de/storage/02dagstuhl-follow-ups/dfu-vol007/DFU.Vol7.15301.327/DFU.Vol7.15301.327.pdf
Quantified constraints
Constraint satisfaction problems
Computational complexity
Parameterized complexity
Universal algebra