Study of Neural Network Algorithm for Straight-Line Drawings of Planar Graphs

TL;DR

This paper presents a new neural network-based method for drawing planar graphs with minimal crossings, focusing on computational efficiency and avoiding heavy preprocessing, using SOM and ISOM techniques.

Contribution

Introduces a novel layout method for planar graphs utilizing neural networks, specifically SOM and ISOM, that reduces computational demands and simplifies the drawing process.

Findings

Efficiently produces straight-line planar graph drawings.

Requires minimal computational resources and preprocessing.

Effective for internally convex planar graphs.

Abstract

Graph drawing addresses the problem of finding a layout of a graph that satisfies given aesthetic and understandability objectives. The most important objective in graph drawing is minimization of the number of crossings in the drawing, as the aesthetics and readability of graph drawings depend on the number of edge crossings. VLSI layouts with fewer crossings are more easily realizable and consequently cheaper. A straight-line drawing of a planar graph G of n vertices is a drawing of G such that each edge is drawn as a straight-line segment without edge crossings. However, a problem with current graph layout methods which are capable of producing satisfactory results for a wide range of graphs is that they often put an extremely high demand on computational resources. This paper introduces a new layout method, which nicely draws internally convex of planar graph that consumes only little computational resources and does not need any heavy duty preprocessing. Here, we use two methods: The first is self organizing map known from unsupervised neural networks which is known as (SOM) and the second method is Inverse Self Organized Map (ISOM).