Parameterizing above guaranteed values: MaxSat and MaxCut
Journal of Algorithms
Parameterized complexity of finding subgraphs with hereditary properties
Theoretical Computer Science
Matching Theory (North-Holland mathematics studies)
Matching Theory (North-Holland mathematics studies)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized graph separation problems
Theoretical Computer Science - Parameterized and exact computation
A fixed-parameter algorithm for the directed feedback vertex set problem
Journal of the ACM (JACM)
Constant ratio fixed-parameter approximation of the edge multicut problem
Information Processing Letters
Almost 2-SAT is fixed-parameter tractable
Journal of Computer and System Sciences
Improved upper bounds for vertex cover
Theoretical Computer Science
Fixed-parameter tractability of multicut parameterized by the size of the cutset
Proceedings of the forty-third annual ACM symposium on Theory of computing
Finding odd cycle transversals
Operations Research Letters
Parameterized Complexity
Generalized above guarantee vertex cover and r-partization
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
On multiway cut parameterized above lower bounds
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
Constraint satisfaction problems parameterized above or below tight bounds: a survey
The Multivariate Algorithmic Revolution and Beyond
Parameterized tractability of multiway cut with parity constraints
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
New races in parameterized algorithmics
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
European Journal of Combinatorics
On multiway cut parameterized above lower bounds
ACM Transactions on Computation Theory (TOCT)
Solving min ones 2-sat as fast as vertex cover
Theoretical Computer Science
Parameterized complexity of MaxSat Above Average
Theoretical Computer Science
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It is well known that in a bipartite (and more generally in a König) graph, the size of the minimum vertex cover is equal to the size of the maximum matching. We first address the question whether (and if not when) this property still holds in a König graph if we insist on forcing one of the two vertices of some of the matching edges in the vertex cover solution. We characterize such graphs using the classical notions of augmenting paths and flowers used in Edmonds' matching algorithm. Using this characterization, we develop an O*(9k) algorithm for the question of whether a general graph has a vertex cover of size at most m+k where m is the size of the maximum matching. Our algorithm for this well studied ABOVE GUARANTEE VERTEX COVER problem uses the technique of iterative compression and the notion of important separators, and improves the runtime of the previous best algorithm that took O*(15k) time. As a consequence of this result we get that well known problems like ALMOST 2 SAT (deleting at most k clauses to get a satisfying 2 SAT formula) and KÖNIG VERTEX DELETION (deleting at most k vertices to get a König graph) also have an algorithm with O*(9k) running time, improving on the previous bound of O*(15k).