Optimizing Wiggle in Storylines

TL;DR

This paper explores optimizing storyline visualizations by minimizing wiggle, introducing algorithms for different wiggle measures, and demonstrating their effectiveness through case studies and a new railway scheduling use case.

Contribution

It presents the first complexity analysis of wiggle minimization and offers efficient algorithms for linear and quadratic wiggle height minimization.

Findings

Wiggle count minimization is NP-complete.

Algorithms for linear and quadratic wiggle minimization are effective.

New railway scheduling visualization case study.

Abstract

A storyline visualization shows interactions between characters over time. Each character is represented by an x-monotone curve. Time is mapped to the x-axis, and groups of characters that interact at a particular point $t$ in time must be ordered consecutively in the y-dimension at $x=t$. The predominant objective in storyline optimization so far has been the minimization of crossings between (blocks of) characters. Building on this work, we investigate another important, but less studied quality criterion, namely the minimization of wiggle, i.e., the amount of vertical movement of the characters over time. Given a storyline instance together with an ordering of the characters at any point in time, we show that wiggle count minimization is NP-complete. In contrast, we provide algorithms based on mathematical programming to solve linear wiggle height minimization and quadratic wiggle height minimization efficiently. Finally, we introduce a new method for routing character curves that focuses on keeping distances between neighboring curves constant as long as they run in parallel. We have implemented our algorithms, and we conduct a case study that explores the differences between the three optimization objectives. We use existing benchmark data, but we also present a new use case for storylines, namely the visualization of rolling stock schedules in railway operation.