Drawing Graphs within Restricted Area

TL;DR

This paper addresses the challenge of selecting maximum-weight subgraphs that can be drawn within a specified area considering non-uniform vertex sizes, proposing heuristics for both general and directed graph cases.

Contribution

It introduces heuristics for drawing subgraphs within restricted areas, applicable to undirected and directed graphs, including calculation graphs for educational analysis.

Findings

Heuristics effectively find subgraphs fitting within the area constraints.

Application to calculation graphs reveals insights into students' mistake patterns.

Method improves graph drawing within spatial limitations.

Abstract

We study the problem of selecting a maximum-weight subgraph of a given graph such that the subgraph can be drawn within a prescribed drawing area subject to given non-uniform vertex sizes. We develop and analyze heuristics both for the general (undirected) case and for the use case of (directed) calculation graphs which are used to analyze the typical mistakes that high school students make when transforming mathematical expressions in the process of calculating, for example, sums of fractions.