Content deleted Content added
→References: add ref |
m dab link |
||
Line 2:
The problem may be visualized as placing the vertices of a graph at distinct integer points along the ''x''-axis so that the length of the longest edge is minimized. Such placement is called '''linear graph arrangement''', '''linear graph layout''' or '''linear graph placement'''.<ref name=feige/>
The '''weighted graph bandwidth problem''' is a generalization wherein the edges are assigned weights ''w<sub>ij</sub>'' and the [[Loss function|cost function]] to be minimized is <math>\max\{\, w_{ij} |f(v_i) - f(v_j)| : v_iv_j \in E \,\}</math>.
In terms of matrices, the (unweighted) graph bandwidth is the [[bandwidth (matrix theory)|bandwidth]] of the [[symmetric matrix]] which is the [[adjacency matrix]] of the graph.
| |||