Years and Authors of Summarized Original Work
2010; R. Crowston, G. Gutin, M. Jones, E.J. Kim, I.Z. Ruzsa
2011; G. Gutin, E.J. Kim, S. Szeider, A. Yeo
2014; R. Crowston, M. Fellows, G. Gutin, M. Jones, E.J. Kim, F. Rosamond, I.Z. Ruzsa, S. Thomassé, A. Yeo
Problem Definition
The problem MaxLin2 can be stated as follows. We are given a system of m equations in variables x 1, …, x n where each equation is \(\prod _{i\in I_{j}}x_{i} = b_{j}\), for some I j ⊆ { 1, 2, …, n} and x i , b j ∈ { − 1, 1} and j = 1, …, m. Each equation is assigned a positive integral weight w j . We are required to find an assignment of values to the variables in order to maximize the total weight of the satisfied equations. MaxLin2 is a well-studied problem, which according to Håstad [8] “is as basic as satisfiability.”
Note that one can think of MaxLin2 as containing equations, \(\sum _{i\in I_{j}}y_{i} = a_{j}\) over \(\mathbb{F}_{2}\). This is equivalent to the previous definition by letting y i = 0 if and...
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Bibliography
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Yeo, A. (2014). Kernelization: MaxLin Above Average. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-3-642-27848-8_532-1
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DOI: https://doi.org/10.1007/978-3-642-27848-8_532-1
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