Abstract
As a problem with similar properties to minimum bisection, we consider the following: given a homogeneous system of linear equations over Z/sub 2/, with exactly k variables in each equation, find a balanced assignment that minimizes the number of satisfied equations. A balanced assignment is one which contains an equal number of 0s and 1s. When k=2, this is the minimum bisection problem. We consider the case k=3. In this case, it is NP-complete to determine whether the object function is zero [U. Feige, (2003)], so the problem is not approximable at all. However, we prove that it is NP-hard to determine distinguish between the cases that all but a fraction /spl epsi/ of the equations can be satisfied and that at least a fraction 1/4-/spl epsi/ of all equations cannot be satisfied. A similar result for minimum bisection would imply that the problem is hard to approximate within any constant. For the problem of approximating the maximum number of equations satisfied by a balanced assignment, this implies that the problem is NP-hard to approximate within 4/3-/spl epsi/, for any /spl epsi/>0.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
