Institut für Informatik   Abteilung V

 Universität Bonn -> Institut für Informatik -> Abteilung V CS-APX-Reports 2001 Copyright 2001 Universität Bonn, Institut für Informatik, Abt. V 8967 April 3, 2001 Approximation Hardness of Bounded Degree MIN-CSP and MIN-BISECTION Piotr Berman and Marek Karpinski [Download PostScript] [Download PDF] We consider bounded occurrence (degree) instances of a minimum constraint satisfaction problem MIN-LIN2 and a MIN-BISECTION problem for graphs. MIN-LIN2 is an optimization problem for a given system of linear equations mod 2 to construct a solution that satisfies the minimum number of them. E3-OCC-MIN-E3-LIN2 is the bounded occurrence (degree) problem restricted as follows: each equation has exactly 3 variables and each variable occurs in exactly 3 equations. Clearly, MIN-LIN2 is equivalent to another well known problem, the Nearest Codeword problem, and E3-OCC-MIN-E3-LIN2 to its bounded occurrence version. MIN-BISECTION is a problem of finding a minimum bisection of a graph, while 3-MIN-BISECTION is the MIN-BISECTION problem restricted to 3-regular graphs only. We show that, somewhat surprisingly, these two restricted problems are exactly as hard to approximate as their general versions. In particular, an approximation ratio lower bound for E3-OCC-MIN-E3-LIN2 (bounded 3-occurrence 3-ary Nearest Codeword problem) is equal to MIN-LIN2 (Nearest Codeword problem) lower bound n^ (Omega(1) / log log n). Moreover, an existence of a constant factor approximation ratio (or a PTAS) for 3-MIN-BISECTION entails existence of a constant approximation ratio (or a PTAS) for the general MIN-BISECTION. Last Change: 11/05/14 at 10:22:22  English Universität Bonn -> Institut für Informatik -> Abteilung V