The complexity of Boolean functions
The complexity of Boolean functions
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Efficient Generation of Minimal Length Addition Chains
SIAM Journal on Computing
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
The macro model for data compression (Extended Abstract)
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Complexity of approximating bounded variants of optimization problems
Theoretical Computer Science - Foundations of computation theory (FCT 2003)
Grammar-based codes: a new class of universal lossless source codes
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Parameterized Complexity
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Given a set of monomials, the Minimum-AND-Circuit problem asks for a circuit that computes these monomials using AND-gates of fan-in two and being of minimum size. We prove that the problem is not polynomial time approximable within a factor of less than 1.0051 unless P = NP, even if the monomials are restricted to be of degree at most three. For the latter case, we devise several efficient approximation algorithms, yielding an approximation ratio of 1.278. For the general problem, we achieve an approximation ratio of d–3/2, where d is the degree of the largest monomial. In addition, we prove that the problem is fixed parameter tractable with the number of monomials as parameter. Finally, we reveal connections between the Minimum AND-Circuit problem and several problems from different areas