Note on Max Lin-2 above Average

In the Max Lin-2 problem we are given a system S of m linear equations in n variables over F2 in which Equation j is assigned a positive integral weight wj for each j. We wish to find an assignment of values to the variables which maximizes the total weight of satisfied equations. This problem generalizes Max Cut. The expected weight of satisfied equations is W/2, where W = w1 + · · · + wm; W/2 is a tight lower bound on the optimal solution of Max Lin-2. Mahajan et al. (J. Comput. Syst. Sci. 75, 2009) stated the following parameterized version of Max Lin-2: decide whether there is an assignment of values to the variables that satisfies equations of total weight at least W/2 + k, where k is the parameter. They asked whether this parameterized problem is fixed-parameter tractable, i.e., can be solved in time f(k)(nm)O(1) , where f(k) is an arbitrary computable function in k only. Their question remains open, but using some probabilistic inequalities and, in one case, a Fourier a...

• Type: Journal
• Year: 2010
• Where: IPL
• Authors: Robert Crowston, Gregory Gutin, Mark Jones
• Keywords: Equations, IPL 2010, Mahajan Et, Max Lin-2