Expected computation time for Hamiltonian path problem
SIAM Journal on Computing
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
The number of maximal independent sets in triangle-free graphs
SIAM Journal on Discrete Mathematics
Inclusion and exclusion algorithm for the Hamiltonian Path Problem
Information Processing Letters
A machine program for theorem-proving
Communications of the ACM
A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Worst-case time bounds for coloring and satisfiability problems
Journal of Algorithms
Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
A determinant-based algorithm for counting perfect matchings in a general graph
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
An algorithm for Exact Satisfiability analysed with the number of clauses as parameter
Information Processing Letters
On some weighted satisfiability and graph problems
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Partitioning based algorithms for some colouring problems
CSCLP'05 Proceedings of the 2005 Joint ERCIM/CoLogNET international conference on Constraint Solving and Constraint Logic Programming
Enumerating maximal independent sets with applications to graph colouring
Operations Research Letters
Improved fixed parameter tractable algorithms for two “edge” problems: MAXCUT and MAXDAG
Information Processing Letters
Exponential-time approximation of weighted set cover
Information Processing Letters
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
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We present exact algorithms with exponential running times for variants of n-element set cover problems, based on divide-and-conquer and on inclusion–exclusion characterisations. We show that the Exact Satisfiability problem of size l with m clauses can be solved in time 2mlO(1) and polynomial space. The same bounds hold for counting the number of solutions. As a special case, we can count the number of perfect matchings in an n-vertex graph in time 2nnO(1) and polynomial space. We also show how to count the number of perfect matchings in time O(1.732n) and exponential space. Using the same techniques we show how to compute Chromatic Number of an n-vertex graph in time O(2.4423n) and polynomial space, or time O(2.3236n) and exponential space.