Fourier meets möbius: fast subset convolution
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Exact and approximate link scheduling algorithms under the physical interference model
Proceedings of the fifth international workshop on Foundations of mobile computing
Algorithms for Counting 2-Sat Solutions and Colorings with Applications
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Iterative Compression and Exact Algorithms
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Combinatorial bounds via measure and conquer: Bounding minimal dominating sets and applications
ACM Transactions on Algorithms (TALG)
A measure & conquer approach for the analysis of exact algorithms
Journal of the ACM (JACM)
Approximation of min coloring by moderately exponential algorithms
Information Processing Letters
Counting Subgraphs via Homomorphisms
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Exact and Approximate Bandwidth
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Polynomial constraint satisfaction problems, graph bisection, and the Ising partition function
ACM Transactions on Algorithms (TALG)
An exact algorithm for subgraph homeomorphism
Journal of Discrete Algorithms
Iterative compression and exact algorithms
Theoretical Computer Science
On exact complexity of subgraph homeomorphism
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
The time complexity of constraint satisfaction
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
A moderately exponential time algorithm for full degree spanning tree
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Exact and approximate bandwidth
Theoretical Computer Science
Dominating set based exact algorithms for 3-coloring
Information Processing Letters
Colorings with few colors: counting, enumeration and combinatorial bounds
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
An exact algorithm for the Boolean connectivity problem for k-CNF
Theoretical Computer Science
Sharp separation and applications to exact and parameterized algorithms
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
An exact algorithm for the boolean connectivity problem for k-CNF
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
Sum-Max graph partitioning problem
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Improved exact algorithms for counting 3- and 4-colorings
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Counting minimum weighted dominating sets
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Trees having many minimal dominating sets
Information Processing Letters
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We use the principle of inclusion and exclusion, combined with polynomial time segmentation and fast Mobius transform, to solve the generic problem of summing or optimizing over the partitions of n elements into a given number of weighted subsets. This problem subsumes various classical graph partitioning problems, such as graph coloring, domatic partitioning, and MAX k-CUT, as well as machine learning problems like decision graph learning and model-based data clustering. Our algorithm runs in O*(2^n ) time, thus substantially improving on the usual O*(3^n )-time dynamic programming algorithm; the notation O* suppresses factors polynomial in n. This result improves, e.g., Byskov's recent record for graph coloring from O*(2.4023^n ) to O*(2^n ). We note that twenty five years ago, R. M. Karp used inclusion--exclusion in a similar fashion to reduce the space requirement of the usual dynamic programming algorithms from exponential to polynomial.