iFlow: An Interactive Max-Flow/Min-Cut Algorithms Visualizer

TL;DR

iFlow is an interactive visualization tool designed to help students better understand the Ford-Fulkerson Max-Flow/Min-Cut algorithm through hands-on simulation and detailed feedback, enhancing learning in educational settings.

Contribution

This paper introduces iFlow, a novel interactive visualization tool for the Ford-Fulkerson algorithm, supporting hands-on learning and auto-completion features for educational use.

Findings

Students found iFlow useful and engaging.

Most students reported increased understanding of the algorithm.

The tool was successfully deployed in an undergraduate class.

Abstract

The Max-Flow/Min-Cut problem is a fundamental tool in graph theory, with applications in many domains, including data mining, image segmentation, transportation planning, and many types of assignment problems, in addition to being an essential building block for many other algorithms. The Ford-Fulkerson Algorithm for Max-Flow/Min-Cut and its variants are therefore commonly taught in undergraduate and beginning graduate algorithms classes. However, these algorithms -- and in particular the so-called residual graphs they utilize -- often pose significant challenges for students. To help students achieve a deeper understanding, we developed iFlow, an interactive visualization tool for the Ford-Fulkerson Algorithm and its variants. iFlow lets users design or import flow networks, and execute the algorithm by hand. In particular, the user can select an augmentation path and amount, and then update the residual graph. The user is given detailed feedback on mistakes, and can also have iFlow auto-complete each step, to use it as a demonstration tool while still in the initial learning stages. iFlow has been made publicly available and open-sourced. We deployed iFlow in an undergraduate algorithms class, and collected students' self-reported learning benefits via an optional survey. All respondents considered the tool at least somewhat useful and engaging, with most rating it either as useful/engaging or very useful/engaging. Students also generally reported a significant increase in understanding of the algorithm.