number optimization problem variables existence system https://doi.org/10.1007/3-540-45465-9_53 Nearest Codeword Problem 623-632 version LIN2 ratio approximation ratio https://scigraph.springernature.com/explorer/license/ general version 2002-06-25 approximation hardness Approximation Hardness of Bounded Degree MIN-CSP and MIN-BISECTION equations Restricted Problem n. 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 nΩ(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. Min-Bisection constant-factor approximation ratio 2002-06-25 constant approximation ratio chapters graph 2022-09-02T16:15 minimum number solution bisection min-bisection problem mod 2 hardness false problem chapter minimum bisection log n. instances Piotr Berman Morales Rafael Mathematical Sciences Marek Karpinski 10.1007/3-540-45465-9_53 doi Eidenbenz Stephan Matthew Hennessy Numerical and Computational Mathematics Ricardo Conejo Widmayer Peter Automata, Languages and Programming 978-3-540-43864-9 978-3-540-45465-6 Dept. of Computer Science, University of Bonn, 53117, Bonn Dept. of Computer Science, University of Bonn, 53117, Bonn Springer Nature Francisco Triguero pub.1026604548 dimensions_id Springer Nature - SN SciGraph project