scholarly journals A note on minimum linear arrangement for BC graphs

2018 ◽  
Vol 10 (02) ◽  
pp. 1850023
Author(s):  
Xiaofang Jiang ◽  
Qinghui Liu ◽  
N. Parthiban ◽  
R. Sundara Rajan
Keyword(s):  
Linear Ordering ◽  
Linear Arrangement ◽  
Arrangement Problem ◽  
Twisted Cube ◽  
Linear Arrangement Problem ◽  
Cube Formula ◽  
Twisted Cubes

A linear arrangement is a labeling or a numbering or a linear ordering of the vertices of a graph. In this paper, we solve the minimum linear arrangement problem for bijective connection graphs (for short BC graphs) which include hypercubes, Möbius cubes, crossed cubes, twisted cubes, locally twisted cube, spined cube, [Formula: see text]-cubes, etc., as the subfamilies.

scholarly journals Tractable Parameterizations for the Minimum Linear Arrangement Problem

2016 ◽  
Vol 8 (2) ◽  
pp. 1-12 ◽  
Author(s):  
Michael R. Fellows ◽  
Danny Hermelin ◽  
Frances Rosamond ◽  
Hadas Shachnai
Keyword(s):  
Linear Arrangement ◽  
Arrangement Problem ◽  
Linear Arrangement Problem

scholarly journals On minimum cuts and the linear arrangement problem

2000 ◽  
Vol 103 (1-3) ◽  
pp. 127-139 ◽  
Author(s):  
S.B. Horton ◽  
R.Gary Parker ◽  
R.B. Borie
Keyword(s):  
Linear Arrangement ◽  
Minimum Cuts ◽  
Arrangement Problem ◽  
Linear Arrangement Problem

On Bipartite Drawings and the Linear Arrangement Problem

2001 ◽  
Vol 30 (6) ◽  
pp. 1773-1789 ◽  
Author(s):  
Farhad Shahrokhi ◽  
Ondrej Sýkora ◽  
László A. Székely ◽  
Imrich Vrto
Keyword(s):  
Linear Arrangement ◽  
Arrangement Problem ◽  
Linear Arrangement Problem

scholarly journals Variable neighborhood search for minimum linear arrangement problem

2016 ◽  
Vol 26 (1) ◽  
pp. 3-16 ◽  
Author(s):  
Nenad Mladenovic ◽  
Dragan Urosevic ◽  
Dionisio Pérez-Brito
Keyword(s):  
Variable Neighborhood Search ◽  
Optimization Problems ◽  
State Of The Art ◽  
The State ◽  
Computational Experiments ◽  
Neighborhood Search ◽  
Np Hard ◽  
Linear Arrangement ◽  
Arrangement Problem ◽  
Linear Arrangement Problem

The minimum linear arrangement problem is widely used and studied in many practical and theoretical applications. It consists of finding an embedding of the nodes of a graph on the line such that the sum of the resulting edge lengths is minimized. This problem is one among the classical NP-hard optimization problems and therefore there has been extensive research on exact and approximative algorithms. In this paper we present an implementation of a variable neighborhood search (VNS) for solving minimum linear arrangement problem. We use Skewed general VNS scheme that appeared to be successful in solving some recent optimization problems on graphs. Based on computational experiments, we argue that our approach is comparable with the state-of-the-art heuristic.

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