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