On the approximation of maximum satisfiability
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
A Geometric Approach to Betweenness
SIAM Journal on Discrete Mathematics
Parameterizing above guaranteed values: MaxSat and MaxCut
Journal of Algorithms
Complexity of Partial Satisfaction
Journal of the ACM (JACM)
A new approach to cyclic ordering of 2D orientations using ternary relation algebras
Artificial Intelligence
Some optimal inapproximability results
Journal of the ACM (JACM)
Vertex cover: further observations and further improvements
Journal of Algorithms
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Voting paradoxes and digraphs realizations
Advances in Applied Mathematics
Polynomial-time recognition of minimal unsatisfiable formulas with fixed clause-variable difference
Theoretical Computer Science
Algorithms with large domination ratio
Journal of Algorithms
On the advantage over a random assignment
Random Structures & Algorithms
Minimal unsatisfiable formulas with bounded clause-variable difference are fixed-parameter tractable
Journal of Computer and System Sciences
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Crown reductions for the Minimum Weighted Vertex Cover problem
Discrete Applied Mathematics
Some topics in analysis of boolean functions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Beating the Random Ordering is Hard: Inapproximability of Maximum Acyclic Subgraph
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Digraphs: Theory, Algorithms and Applications
Digraphs: Theory, Algorithms and Applications
Every Permutation CSP of arity 3 is Approximation Resistant
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
On problems without polynomial kernels
Journal of Computer and System Sciences
Almost 2-SAT is fixed-parameter tractable
Journal of Computer and System Sciences
Note on Max Lin-2 above Average
Information Processing Letters
Betweenness parameterized above tight lower bound
Journal of Computer and System Sciences
A probabilistic approach to problems parameterized above or below tight bounds
Journal of Computer and System Sciences
Extremal Combinatorics: With Applications in Computer Science
Extremal Combinatorics: With Applications in Computer Science
Kernel bounds for disjoint cycles and disjoint paths
Theoretical Computer Science
A new bound for 3-satisfiable maxsat and its algorithmic application
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Paths, flowers and vertex cover
ESA'11 Proceedings of the 19th European conference on Algorithms
A kernel of order 2k-clogk for vertex cover
Information Processing Letters
Journal of Computer and System Sciences
Beating the Random Ordering Is Hard: Every Ordering CSP Is Approximation Resistant
SIAM Journal on Computing
Solving MAX-r-SAT Above a Tight Lower Bound
Algorithmica
Systems of linear equations over F2 and problems parameterized above average
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Parameterizing MAX SNP problems above guaranteed values
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Improved parameterized algorithms for above average constraint satisfaction
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
On the hardness of losing width
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Parameterized complexity of maxsat above average
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Communication: Hypercontractive inequality for pseudo-Boolean functions of bounded Fourier width
Discrete Applied Mathematics
Parameterized Complexity
A basic parameterized complexity primer
The Multivariate Algorithmic Revolution and Beyond
Bisections above tight lower bounds
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
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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 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, ri 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 of arities 2 and 3 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.