A fast and simple randomized parallel algorithm for the maximal independent set problem
Journal of Algorithms
Journal of the ACM (JACM)
Communication complexity
The Parameterized Complexity of Counting Problems
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Dispersion of Mass and the Complexity of Randomized Geometric Algorithms
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Improved algorithms for path, matching, and packing problems
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Partial vs. Complete Domination: t-Dominating Set
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
On Problems without Polynomial Kernels (Extended Abstract)
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Faster Algebraic Algorithms for Path and Packing Problems
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Finding paths of length k in O∗(2k) time
Information Processing Letters
A New Algorithm for Finding Trees with Many Leaves
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Finding, minimizing, and counting weighted subgraphs
Proceedings of the forty-first annual ACM symposium on Theory of computing
A faster parameterized algorithm for set packing
Information Processing Letters
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
An Amortized Search Tree Analysis for k-Leaf Spanning Tree
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Counting stars and other small subgraphs in sublinear time
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Exact parameterized multilinear monomial counting via k-layer subset convolution and k-disjoint
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Fast zeta transforms for lattices with few irreducibles
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Shortest cycle through specified elements
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
On the parameterized complexity of the repetition free longest common subsequence problem
Information Processing Letters
Faster algorithms for finding and counting subgraphs
Journal of Computer and System Sciences
A faster exact algorithm for the directed maximum leaf spanning tree problem
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Finding maximum colorful subtrees in practice
RECOMB'12 Proceedings of the 16th Annual international conference on Research in Computational Molecular Biology
Constrained multilinear detection for faster functional motif discovery
Information Processing Letters
Nearly exact mining of frequent trees in large networks
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part I
Homomorphic hashing for sparse coefficient extraction
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Fast monotone summation over disjoint sets
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Finding the minimum-weight k-path
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
On Enumerating Monomials and Other Combinatorial Structures by Polynomial Interpolation
Theory of Computing Systems
Fast monotone summation over disjoint sets
Information Processing Letters
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The algebraic framework introduced in [Koutis, Proc. of the 35 th ICALP 2008] reduces several combinatorial problems in parameterized complexity to the problem of detecting multilinear degree-k monomials in polynomials presented as circuits. The best known (randomized) algorithm for this problem requires only O *(2 k ) time and oracle access to an arithmetic circuit, i.e. the ability to evaluate the circuit on elements from a suitable group algebra. This algorithm has been used to obtain the best known algorithms for several parameterized problems. In this paper we use communication complexity to show that the O *(2 k ) algorithm is essentially optimal within this evaluation oracle framework. On the positive side, we give new applications of the method: finding a copy of a given tree on k nodes, a spanning tree with at least k leaves, a minimum set of nodes that dominate at least t nodes, and an m -dimensional k -matching. In each case we achieve a faster algorithm than what was known. We also apply the algebraic method to problems in exact counting. Among other results, we show that a combination of dynamic programming and a variation of the algebraic method can break the trivial upper bounds for exact parameterized counting in fairly general settings.