Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
SIAM Journal on Computing
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
Simple analysis of graph tests for linearity and PCP
Random Structures & Algorithms
Testing subgraphs in large graphs
Random Structures & Algorithms - Special issue: Proceedings of the tenth international conference "Random structures and algorithms"
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Testing subgraphs in directed graphs
Journal of Computer and System Sciences - Special issue: STOC 2003
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
A Duality between Clause Width and Clause Density for SAT
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
On the Compressibility of NP Instances and Cryptographic Applications
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
A Characterization of Easily Testable Induced Subgraphs
Combinatorics, Probability and Computing
Invitation to data reduction and problem kernelization
ACM SIGACT News
The PCP theorem by gap amplification
Journal of the ACM (JACM)
Random $k$-SAT: Two Moments Suffice to Cross a Sharp Threshold
SIAM Journal on Computing
Infeasibility of instance compression and succinct PCPs for NP
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Testing Triangle-Freeness in General Graphs
SIAM Journal on Discrete Mathematics
A quadratic kernel for feedback vertex set
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
On problems without polynomial kernels
Journal of Computer and System Sciences
Two Edge Modification Problems without Polynomial Kernels
Parameterized and Exact Computation
An improved kernelization algorithm for r-Set Packing
Information Processing Letters
Preprocessing of min ones problems: a dichotomy
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Improved deterministic algorithms for weighted matching and packing problems
Theoretical Computer Science
On the small cycle transversal of planar graphs
Theoretical Computer Science
Kernel bounds for disjoint cycles and disjoint paths
Theoretical Computer Science
A generalization of Nemhauser and Trotter's local optimization theorem
Journal of Computer and System Sciences
Kernels for feedback arc set in tournaments
Journal of Computer and System Sciences
Data reduction for graph coloring problems
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
A kernel of order 2k-clogk for vertex cover
Information Processing Letters
Kernelization of packing problems
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Linear kernels for (connected) dominating set on H-minor-free graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Compression via matroids: a randomized polynomial kernel for odd cycle transversal
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Weak compositions and their applications to polynomial lower bounds for kernelization
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Co-nondeterminism in compositions: a kernelization lower bound for a Ramsey-type problem
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Kernelization for cycle transversal problems
Discrete Applied Mathematics
A polynomial kernel for feedback arc set on bipartite tournaments
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Safe approximation and its relation to kernelization
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Discrete Optimization
Some remarks on the incompressibility of width-parameterized SAT instances
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Kernels for packing and covering problems
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Kernelization --- preprocessing with a guarantee
The Multivariate Algorithmic Revolution and Beyond
What's next? future directions in parameterized complexity
The Multivariate Algorithmic Revolution and Beyond
Kernel(s) for problems with no kernel: On out-trees with many leaves
ACM Transactions on Algorithms (TALG)
Kernelization hardness of connectivity problems in d-degenerate graphs
Discrete Applied Mathematics
Clique cover and graph separation: new incompressibility results
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
A linear kernel for the complementary maximal strip recovery problem
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Kernel lower bounds using co-nondeterminism: finding induced hereditary subgraphs
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Polynomial kernels for dominating set in graphs of bounded degeneracy and beyond
ACM Transactions on Algorithms (TALG)
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
Data reduction for graph coloring problems
Information and Computation
A Polynomial Kernel for Feedback Arc Set on Bipartite Tournaments
Theory of Computing Systems
Preprocessing subgraph and minor problems: When does a small vertex cover help?
Journal of Computer and System Sciences
Kernel bounds for path and cycle problems
Theoretical Computer Science
Theoretical Computer Science
Towards optimal kernel for edge-disjoint triangle packing
Information Processing Letters
Hi-index | 0.01 |
Consider the following two-player communication process to decide a language L: The first player holds the entire input x but is polynomially bounded; the second player is computationally unbounded but does not know any part of x; their goal is to cooperatively decide whether x belongs to L at small cost, where the cost measure is the number of bits of communication from the first player to the second player. For any integer d ≥ 3 and positive real ε we show that if satisfiability for n-variable d-CNF formulas has a protocol of cost O(nd-ε) then coNP is in NP/poly, which implies that the polynomial-time hierarchy collapses to its third level. The result even holds when the first player is conondeterministic, and is tight as there exists a trivial protocol for ε = 0. Under the hypothesis that coNP is not in NP/poly, our result implies tight lower bounds for parameters of interest in several areas, namely sparsification, kernelization in parameterized complexity, lossy compression, and probabilistically checkable proofs. By reduction, similar results hold for other NP-complete problems. For the vertex cover problem on n-vertex d-uniform hypergraphs, the above statement holds for any integer d ≥ 2. The case d=2 implies that no NP-hard vertex deletion problem based on a graph property that is inherited by subgraphs can have kernels consisting of O(k2-ε) edges unless coNP is in NP/poly, where k denotes the size of the deletion set. Kernels consisting of O(k^2) edges are known for several problems in the class, including vertex cover, feedback vertex set, and bounded-degree deletion.