Exact and approximate link scheduling algorithms under the physical interference model
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Efficient approximation of min set cover by moderately exponential algorithms
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ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Efficient Approximation of Combinatorial Problems by Moderately Exponential Algorithms
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
New Plain-Exponential Time Classes for Graph Homomorphism
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
Exact Algorithms for Set Multicover and Multiset Multicover Problems
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
On Partitioning a Graph into Two Connected Subgraphs
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Dynamic programming based algorithms for set multicover and multiset multicover problems
Theoretical Computer Science
On the complexity of circuit satisfiability
Proceedings of the forty-second ACM symposium on Theory of computing
Saving space by algebraization
Proceedings of the forty-second ACM symposium on Theory of computing
Covering and packing in linear space
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Feedback vertex sets in tournaments
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Partition into triangles on bounded degree graphs
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Collective spatial keyword querying
Proceedings of the 2011 ACM SIGMOD International Conference on Management of data
Breaking the 2n-barrier for Irredundance: Two lines of attack
Journal of Discrete Algorithms
Channel assignment via fast zeta transform
Information Processing Letters
Invitation to algorithmic uses of inclusion-exclusion
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
On the partition of 3-colorable graphs
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Covering and packing in linear space
Information Processing Letters
Scheduling partially ordered jobs faster than 2n
ESA'11 Proceedings of the 19th European conference on Algorithms
On partitioning a graph into two connected subgraphs
Theoretical Computer Science
Counting perfect matchings as fast as Ryser
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Fast zeta transforms for lattices with few irreducibles
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Computing hypergraph width measures exactly
Information Processing Letters
Polynomial space algorithms for counting dominating sets and the domatic number
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Counting independent sets in claw-free graphs
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Counting maximal independent sets in subcubic graphs
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
An exact exponential time algorithm for counting bipartite cliques
Information Processing Letters
Solving the 2-disjoint connected subgraphs problem faster than 2n
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Approximating MAX SAT by moderately exponential and parameterized algorithms
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Algorithms for dominating clique problems
Theoretical Computer Science
On the parameterized complexity of the workflow satisfiability problem
Proceedings of the 2012 ACM conference on Computer and communications security
Feedback Vertex Sets in Tournaments
Journal of Graph Theory
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
Regular inference as vertex coloring
ALT'12 Proceedings of the 23rd international conference on Algorithmic Learning Theory
Efficient algorithms for the max k-vertex cover problem
TCS'12 Proceedings of the 7th IFIP TC 1/WG 202 international conference on Theoretical Computer Science
Determining the l(2,1)-span in polynomial space
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Communications of the ACM
On the Parameterized Complexity and Kernelization of the Workflow Satisfiability Problem
ACM Transactions on Information and System Security (TISSEC)
Determining the L(2,1)-span in polynomial space
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Nonuniform ACC Circuit Lower Bounds
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Exact algorithm for graph homomorphism and locally injective graph homomorphism
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Hi-index | 0.03 |
Given a set $N$ with $n$ elements and a family $\mathcal{F}$ of subsets, we show how to partition $N$ into $k$ such subsets in $2^n n^{O(1)}$ time. We also consider variations of this problem where the subsets may overlap or are weighted, and we solve the decision, counting, summation, and optimization versions of these problems. Our algorithms are based on the principle of inclusion-exclusion and the zeta transform. In effect we get exact algorithms in $2^n n^{O(1)}$ time for several well-studied partition problems including domatic number, chromatic number, maximum $k$-cut, bin packing, list coloring, and the chromatic polynomial. We also have applications to Bayesian learning with decision graphs and to model-based data clustering. If only polynomial space is available, our algorithms run in time $3^n n^{O(1)}$ if membership in $\mathcal{F}$ can be decided in polynomial time. We solve chromatic number in $O(2.2461^n)$ time and domatic number in $O(2.8718^n)$ time. Finally, we present a family of polynomial space approximation algorithms that find a number between $\chi(G)$ and $\lceil(1+\epsilon)\chi(G)\rceil$ in time $O(1.2209^n+2.2461^{e^{-\epsilon}n})$.