Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
.879-approximation algorithms for MAX CUT and MAX 2SAT
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Randomized algorithms
On fixed-parameter tractability and approximability of NP optimization problems
Journal of Computer and System Sciences - special issue on complexity theory
On Syntactic versus Computational Views of Approximability
SIAM Journal on Computing
Parameterizing above guaranteed values: MaxSat and MaxCut
Journal of Algorithms
New upper bounds for maximum satisfiability
Journal of Algorithms
On the advantage over a random assignment
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Approximating Minimum-Size k-Connected Spanning Subgraphs via Matching
SIAM Journal on Computing
Parameterized complexity of finding subgraphs with hereditary properties
Theoretical Computer Science
Combinatorica
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Faster fixed parameter tractable algorithms for finding feedback vertex sets
ACM Transactions on Algorithms (TALG)
Minimum Bounded Degree Spanning Trees
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Interval completion with few edges
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Almost 2-SAT Is Fixed-Parameter Tractable (Extended Abstract)
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Obtaining a planar graph by vertex deletion
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
The complexity of finding subgraphs whose matching number equals the vertex cover number
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Wheel-free deletion is W[2]-hard
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Chordal deletion is fixed-parameter tractable
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
The linear arrangement problem parameterized above guaranteed value
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Parameterizing MAX SNP problems above guaranteed values
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Fixed-parameter complexity of minimum profile problems
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Fixed-parameter approximation: conceptual framework and approximability results
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
On parameterized approximability
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Parameterized approximation problems
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Finding odd cycle transversals
Operations Research Letters
Note on Max Lin-2 above Average
Information Processing Letters
Note on maximal bisection above tight lower bound
Information Processing Letters
Betweenness parameterized above tight lower bound
Journal of Computer and System Sciences
Solving MAX-r-SAT above a tight lower bound
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
A probabilistic approach to problems parameterized above or below tight bounds
Journal of Computer and System Sciences
Ranking and drawing in subexponential time
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
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
Journal of Computer and System Sciences
Systems of linear equations over F2 and problems parameterized above average
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Generalized above guarantee vertex cover and r-partization
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
Improved parameterized algorithms for above average constraint satisfaction
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
New lower bound on max cut of hypergraphs with an application to r-set splitting
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
The impact of parameterized complexity to interdisciplinary problem solving
The Multivariate Algorithmic Revolution and Beyond
Studies in computational aspects of voting: open problems of downey and fellows
The Multivariate Algorithmic Revolution and Beyond
Communication: Hypercontractive inequality for pseudo-Boolean functions of bounded Fourier width
Discrete Applied Mathematics
Max-cut parameterized above the edwards-erdős bound
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Parameterized study of the test cover problem
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Parameterized complexity of MaxSat Above Average
Theoretical Computer Science
Maximum balanced subgraph problem parameterized above lower bound
Theoretical Computer Science
Satisfying more than half of a system of linear equations over GF(2): A multivariate approach
Journal of Computer and System Sciences
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We consider new parameterizations of NP-optimization problems that have nontrivial lower and/or upper bounds on their optimum solution size. The natural parameter, we argue, is the quantity above the lower bound or below the upper bound. We show that for every problem in MAX SNP, the optimum value is bounded below by an unbounded function of the input-size, and that the above-guarantee parameterization with respect to this lower bound is fixed-parameter tractable. We also observe that approximation algorithms give nontrivial lower or upper bounds on the solution size and that the above or below guarantee question with respect to these bounds is fixed-parameter tractable for a subclass of NP-optimization problems. We then introduce the notion of 'tight' lower and upper bounds and exhibit a number of problems for which the above-guarantee and below-guarantee parameterizations with respect to a tight bound is fixed-parameter tractable or W-hard. We show that if we parameterize ''sufficiently'' above or below the tight bounds, then these parameterized versions are not fixed-parameter tractable unless P=NP, for a subclass of NP-optimization problems. We also list several directions to explore in this paradigm.