# Constraint Satisfaction Problems Parameterized above or below Tight Bounds: A Survey

@inproceedings{Gutin2012ConstraintSP, title={Constraint Satisfaction Problems Parameterized above or below Tight Bounds: A Survey}, author={Gregory Gutin and Anders Yeo}, booktitle={The Multivariate Algorithmic Revolution and Beyond}, year={2012} }

We consider constraint satisfaction problems parameterized above or below tight bounds. 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 $\mathbb{F}_2$ in which each equation has a positive integral weight, decide whether there is an assignment to the variables…

## 30 Citations

Parameterized Constraint Satisfaction Problems: a Survey

- MathematicsThe Constraint Satisfaction Problem
- 2017

This work considers constraint satisfaction problems parameterized above or below guaranteed values, both polynomial kernels and parameterized algorithms, and discusses results and questions obtained for the problems mainly in the last few years.

Satisfiability of Ordering CSPs above Average is Fixed-Parameter Tractable

- Mathematics, Computer Science2015 IEEE 56th Annual Symposium on Foundations of Computer Science
- 2015

A new Bonami-type inequality for the Efron -- Stein decomposition is proved, which applies to functions defined on arbitrary product probability spaces and does not depend on the mass of the smallest atom in the probability space.

Satisfiability of Ordering CSPs Above Average

- Mathematics, Computer ScienceArXiv
- 2015

A new Bonami-type inequality for the Efron-Stein decomposition is proved that applies to functions defined on arbitrary product probability spaces and does not depend on the mass of the smallest atom in the probability space.

The Constraint Satisfaction Problem: Complexity and Approximability

- Computer ScienceThe Constraint Satisfaction Problem
- 2017

This report documents the material presented during the course of the Dagstuhl Seminar 18231 “The Constraint Satisfaction Problem: Complexity and Approximability”, aimed at bringing together researchers using all the different techniques in the study of the CSP to share their insights obtained.

Parameterized Traveling Salesman Problem: Beating the Average

- MathematicsSIAM J. Discret. Math.
- 2016

A considerable generalization of Vizing's result is proved: for each fixed $k$, an algorithm is given that decides whether, for any input edge weighting of $K_n$, there is a Hamilton cycle of weight at most $h(w)-k$ (and constructs such a cycle if it exists).

Parameterized TSP: Beating the Average

- MathematicsArXiv
- 2014

A considerable generalisation of Vizing's result is proved: for each fixed $k$, an algorithm is given that decides whether, for any input edge weighting of $K_n$, there is a Hamilton cycle of weight at most $h(w)-k$ (and constructs such a cycle if it exists).

Improved Exact Algorithms for Mildly Sparse Instances of Max SAT

- Computer ScienceIPEC
- 2015

The first result is a deterministic polynomial space algorithm with mu(c)=1/O(c * log(c)) that achieves the previous best time complexity without exponential space or randomization and can handle instances with exponentially large weights and hard constraints.

The Parameterized Complexity of Cycle Packing: Indifference is Not an Issue

- Mathematics, Computer ScienceLATIN
- 2018

This paper shows that Cycle Packing is fixed-parameter tractable (FPT) when parameterized by t, the size of a proper interval deletion set, and combines color coding, greedy strategy and dynamic programming based on structural properties of proper interval graphs in a non-trivial fashion to obtain the FPT algorithm.

Kernelization, MaxLin Above Average

- MathematicsEncyclopedia of Algorithms
- 2016

The problem MAXLIN2 is a well-studied problem, which according to Hastad [8] “is as basic as satisfiability” and the basic definitions of fixed-parameter tractability (FPT) are given.

Improved exact algorithms for mildly sparse instances of Max SAT

- Computer ScienceTheor. Comput. Sci.
- 2017

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