Monte-Carlo approximation algorithms for enumeration problems
Journal of Algorithms
Using hard problems to create pseudorandom generators
Using hard problems to create pseudorandom generators
Journal of the ACM (JACM)
Randomized algorithms
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Parameterizing above guaranteed values: MaxSat and MaxCut
Journal of Algorithms
The Parameterized Complexity of Counting Problems
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Parameterized Counting Problems
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Parameterized Complexity of Finding Subgraphs with Hereditary Properties
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
On Limited versus Polynomial Nondeterminism
On Limited versus Polynomial Nondeterminism
Monte-Carlo algorithms for enumeration and reliability problems
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Parameterized Complexity
The complexity of counting homomorphisms seen from the other side
Theoretical Computer Science
Approximately Counting Embeddings into Random Graphs
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
The parameterized complexity of probability amplification
Information Processing Letters
Approximating the Number of Network Motifs
WAW '09 Proceedings of the 6th International Workshop on Algorithms and Models for the Web-Graph
Finding, minimizing, and counting weighted subgraphs
Proceedings of the forty-first annual ACM symposium on Theory of computing
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Balanced families of perfect hash functions and their applications
ACM Transactions on Algorithms (TALG)
Quantifying systemic evolutionary changes by color coding confidence-scored PPI networks
WABI'09 Proceedings of the 9th international conference on Algorithms in bioinformatics
Counting stars and other small subgraphs in sublinear time
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Parameterized complexity of generalized vertex cover problems
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
The parameterized complexity of maximality and minimality problems
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Randomized approximations of parameterized counting problems
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
On the effective enumerability of NP problems
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
The parameterized complexity of enumerating frequent itemsets
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Balanced families of perfect hash functions and their applications
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
A randomized approximation algorithm for parameterized 3-D matching counting problem
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Parameterized top-K algorithms
Theoretical Computer Science
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We give a randomized fixed parameter tractable algorithm to approximately count the number of copies of a k-vertex graph with bounded treewidth in an n vertex graph. As a consequence, we get randomized algorithms with running time kO(k) nO(1), approximation ratio 1/kO(k), and error probability 2-nO(1) for (a) approximately counting the number of matchings of size k in an n vertex graph and (b) approximately counting the number of paths of length k in an n vertex graph. Our algorithm is based on the Karp-Luby approximate counting technique [8] applied to fixed parameter tractable problems, and the color-coding technique of Alon, Yuster and Zwick [1]. We also show some W-hardness results for parameterized exact counting problems.