On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
WABI '02 Proceedings of the Second International Workshop on Algorithms in Bioinformatics
O(√log n) approximation algorithms for min UnCut, min 2CNF deletion, and directed cut problems
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Parameterized graph separation problems
Theoretical Computer Science - Parameterized and exact computation
Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization
Journal of Computer and System Sciences
Invitation to data reduction and problem kernelization
ACM SIGACT News
Planar graph bipartization in linear time
Discrete Applied Mathematics
A fixed-parameter algorithm for the directed feedback vertex set problem
Journal of the ACM (JACM)
The Complexity Ecology of Parameters: An Illustration Using Bounded Max Leaf Number
Theory of Computing Systems - Special Issue: Computation and Logic in the Real World; Guest Editors: S. Barry Cooper, Elvira Mayordomo and Andrea Sorbi
On problems without polynomial kernels
Journal of Computer and System Sciences
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
An (almost) linear time algorithm for odd cycles transversal
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Infeasibility of instance compression and succinct PCPs for NP
Journal of Computer and System Sciences
Proceedings of the forty-third annual ACM symposium on Theory of computing
Fixed-parameter tractability of multicut parameterized by the size of the cutset
Proceedings of the forty-third annual ACM symposium on Theory of computing
Preprocessing for treewidth: a combinatorial analysis through kernelization
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Improved exact exponential algorithms for vertex bipartization and other problems
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
Two-Layer planarization parameterized by feedback edge set
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
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
European Journal of Combinatorics
Preprocessing subgraph and minor problems: when does a small vertex cover help?
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Preprocessing subgraph and minor problems: When does a small vertex cover help?
Journal of Computer and System Sciences
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The Odd Cycle Transversal problem (OCT) asks whether a given graph can be made bipartite (i.e., 2-colorable) by deleting at most ℓ vertices. We study structural parameterizations of OCT with respect to their polynomial kernelizability, i.e., whether instances can be efficiently reduced to a size polynomial in the chosen parameter. It is a major open problem in parameterized complexity whether Odd Cycle Transversal admits a polynomial kernel when parameterized by ℓ. On the positive side, we show a polynomial kernel for OCT when parameterized by the vertex deletion distance to the class of bipartite graphs of treewidth at most w (for any constant w); this generalizes the parameter feedback vertex set number (i.e., the distance to a forest). Complementing this, we exclude polynomial kernels for OCT parameterized by the distance to outerplanar graphs, conditioned on the assumption that NP ⊈ coNP/poly. Thus the bipartiteness requirement for the treewidth w graphs is necessary. Further lower bounds are given for parameterization by distance from cluster and co-cluster graphs respectively, as well as for Weighted OCT parameterized by the vertex cover number (i.e., the distance from an independent set).