Scalability in Visualization

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SCALABILITY IN VISUALIZATION 1

Ga¨

elle Richer, Alexis Pister, Moataz Abdelaal, Jean-Daniel Fekete, Michael Sedlmair, and Daniel Weiskopf

Abstract—We introduce a conceptual model for scalability designed for visualization research. With this model, we systematically

analyze over 120 visualization publications from 1990 to 2020 to characterize the different notions of scalability in these works. While

many papers have addressed scalability issues, our survey identiﬁes a lack of consistency in the use of the term in the visualization

research community. We address this issue by introducing a consistent terminology meant to help visualization researchers better

characterize the scalability aspects in their research. It also helps in providing multiple methods for supporting the claim that a work is

“scalable.” Our model is centered around an effort function with inputs and outputs. The inputs are the problem size and resources,

whereas the outputs are the actual efforts, for instance, in terms of computational run time or visual clutter. We select representative

examples to illustrate different approaches and facets of what scalability can mean in visualization literature. Finally, targeting the diverse

crowd of visualization researchers without a scalability tradition, we provide a set of recommendations for how scalability can be

presented in a clear and consistent way to improve fair comparison between visualization techniques and systems and foster

reproducibility.

Index Terms—Scalability, visualization, structured literature analysis, conceptual framework

1 INTRODUCTION

We address the issue of characterizing scalability in visu-

alization research. Scalability is a frequent topic, with many

papers claiming to improve scalability or achieve scalable—or

sometimes, more scalable—techniques. The visualization research

community has a long tradition of acknowledging the need for

scalable solutions, as for example, included in summaries of grand

research challenges for various communities of visualization [1],

[2] or roadmaps for future research [3], [4].

Despite the high relevance of scalability—or maybe, because

of this—we noticed a large range of connotations or uses of this

concept in visualization papers. This situation reﬂects the large

diversity of research topics and methods in visualization, and it

may also be the multidisciplinary nature of visualization, which

includes research from computer science and algorithms, human-

computer interaction, psychology, etc. Some of these communities

have established models and methods for assessing scalability,

but not all of them. However, even when such approaches might

be established in another community, they might not necessarily

be common knowledge in the visualization research community.

Furthermore, it is not always clear whether a wholesale adoption

of these methods is possible or if they need to be adapted and

ﬁne-tuned to the speciﬁcities of visualization research.

In short, there is a wide range of interpretations of the

concept of scalability in visualization, sometimes with only implicit

documentation and communication of the concrete interpretation

used in a paper. This can lead to misunderstandings and impair the

reproducibility of research results.

•

G. Richer, A. Pister, and J.-D. Fekete are with Universit

e Paris-Saclay,

CNRS, Inria, LISN, France. A. Pister is also with I3, CNRS, Telecom Paris,

Institut Polytechnique de Paris, France.

E-mail: {ﬁrst-name.last-name}@inria.fr

•

M. Adbelaal, M. Sedlmair, and D. Weiskopf are with University of Stuttgart,

Germany.

E-mail: {ﬁrst-name.last-name}@visus.uni-stuttgart.de

Manuscript received xx xxx. 201x; accepted xx xxx. 201x. Date of Publication

xx xxx. 201x; date of current version xx xxx. 201x. For information on obtaining

reprints of this article, please send e-mail to: reprints@ieee.org. Digital Object

Identiﬁer: xx.xxxx/TVCG.201x.xxxxxxx.

The recent restructuring of the IEEE VIS conferences into

a single conference with multiple areas attests that visualization

research is becoming more diverse and trying to be more integrated.

While some articles will remain targeted to a distinct audience

well aware of its own meaning of scalability, a growing number

of articles will cross boundaries to address multiple meanings of

scalability, leading to more diverse reviewers and readers, with

different backgrounds. We aim at helping authors, reviewers, and

readers navigate the different aspects of scalability.

To this end, we contribute a conceptual model for scalability

that is designed to be versatile and ﬂexible enough to capture exist-

ing uses of the concept ‘scalability’ in visualization research, align

terminology, improve conceptual and methodological consistency

across domains, and allow for other uses in the future. In particular,

we envision the model to help communicate about scalability across

the diverse subcommunities of visualization. Our model is built

on an effort function that takes inputs in the form of problem size,

assumptions, and descriptions of resources, and maps these to a

description of effort as the output associated with the visualization.

Key to the ﬂexibility of the model is the large freedom in modeling

the inputs and outputs: they can cover technical aspects such as data

set size, available compute nodes, or compute times, all the way to

human-oriented aspects like readability or user task performance.

Therefore, we are able to show that this model can be instantiated to

cover the typical scenarios of scalability in visualization, and also

the different interpretations of the terms “scalability,” “scalable,”

and “more scalable.”

We argue that seeking the common traits between the multiple

existing deﬁnitions and presenting them with a uniﬁed model

creates a helpful framework for comprehension. We recognize

our model would not help authors and reviewers within their

subﬁeld, e.g., visualization in high-performance computing (HPC)

or graph drawing, since they have a clear understanding of their

own meaning of scalability. However, it becomes useful for articles

mixing two aspects of scalability, e.g., how HPC can provide

more readable features, with a need to be understood by the two

subcommunities. This kind of scenario is becoming more frequent

in visualization and this is why we need a unifying model.

arXiv:2210.06562v2 [cs.HC] 14 Dec 2022

SCALABILITY IN VISUALIZATION 2

Using the conceptual model as a framework, we analyzed the

current state of visualization research and contribute a structured

and systematic literature analysis of the full papers published in

IEEE Visualization, SciVis, InfoVis, and VAST from 1990 to 2020.

The literature search led to 127 articles for which we derived

a coding scheme and analyzed them, respectively. Four of the

authors participated in multiple rounds of reviews of these relevant

papers followed by discussions to establish the conceptual model,

scenarios, and coding scheme. The two other authors coded the

complete set of papers after being introduced to the coding scheme.

Our goal was to learn about the current usage of the notion of

scalability in visualization research, as well as to assess how well

our conceptual model allows characterizing previous research on

scalability. We make the coding book and results publicly available

at the following repository: https://osf.io/xrvu7/.

Based on our conceptual model, general observations, and

the literature review, we arrive at recommendations to improve

the design and presentation of scalability-related research when

targeting an outside or mixed audience. We believe that this would

also help compare visualization techniques and systems, and foster

reproducibility.

2 RELATED WORK

The visualization research community has become more diverse

over the years, starting with statistics, algorithms, computer

graphics, and computational science in the early 1990s, and joined

by human-computer interaction (HCI), psychology, vision science,

design, cartography, and many more. The concept of scalability

varies from one community to the next, with different levels of

maturity. In this section, we review related work discussing and

deﬁning scalability in different areas of computer science and in

the visualization community.

2.1 Deﬁnitions of Scalability

Weinstock and Goodenough [5] deﬁne the scalability problem as

“the inability of a system to accommodate an increased workload.”

Bondi [6] mentions several deﬁnitions of scalability in computer

science:

•

“Scalability is the property of a system to handle a growing

amount of work by adding resources to the system.” Adding

resources may have the form of adding more nodes to a system

made of multiple small interconnected servers (scaling out

or horizontally) or adding more resources to a single node

(scaling up or vertically) [7].

•

Load scalability is the “ability to function gracefully, i.e.,

without undue delay and without unproductive resource

consumption or resource contention at light, moderate, or

heavy loads while making good use of available resources.”

•

Space scalability is that “memory requirements do not grow to

intolerable levels as the number of items it supports increase.”

•

Space-time scalability: “continues to function gracefully as

the number of objects [. . . ] increases by orders of magnitude.”

•

Structural scalability means that “implementation or standards

do not impede the growth of the number of objects it

encompasses, or at least will not do so within a chosen time

frame.”

Parallel systems and HPC distinguish mainly two types of scalabil-

ity:

•

Strong scaling: “how the solution time varies with the number

of processors for a ﬁxed total problem size.”

•

Weak scaling: “how the solution time varies with the number

of processors for a ﬁxed problem size per processor.”

Hill [8] tries to deﬁne scalability for multiprocessor systems and

admits: “but I fail to ﬁnd a useful, rigorous deﬁnition of it.” Duboc

et al. [9] deﬁne it as: “a quality of software systems characterized

by the causal impact that scaling aspects of the system environment

and design have on certain measured system qualities as these

aspects are varied over expected operational ranges. If the system

can accommodate this variation in a way that is acceptable to the

stakeholder, then it is a scalable system.”

All the deﬁnitions are speciﬁed as properties of systems

at an abstract level, focusing on “amount of work,” “delay,”

“resources,” “productive resource consumption,” “[work]loads,”

“memory,” “function gracefully,” “time frame,” “adding nodes,”

and “shared memory.” They rely on implicit domain knowledge to

be clearly understood and are not suitable to the wide audience of

visualization practitioners.

2.2 Scalability in Visualization and Visual Analytics

Visualization and visual analytics are concerned with general

computer science scalability when it comes to systems or algo-

rithms. In addition, they are also concerned with more speciﬁc

issues. Robertson et al. [10] mention information scalability, visual

scalability, display scalability, and human scalability, in addition

to computational scalability. They also add other scalability issues:

software scalability, temporal scalability, cross-scale issues, privacy

and security issues (related to scale), and language issues. Yost and

North [11] also mention graphical scalability (“limits imposed

by the number of pixels”) and perceptual scalability (“When

the screen is not the limiting factor, just how much data can a

person effectively perceive?”). Eick and Karr [12] want to quantify

visual scalability by modeling the dependence between responses,

factors, and data. They admit that it cannot be done because few

responses can be quantiﬁed or measured. Instead, they break down

the problem into subparts affecting the overall scalability, adding

“visual metaphors,” “interactivity,” and “aggregation” to the list of

factors affecting scalability.

Scalability is also related to evaluation since it is based on

measuring efﬁciency. Lam et al. [13] describe seven scenarios for

evaluation in visualization, some of them leading to quantitative

results and others to qualitative ones. Scalability is part of the

“Evaluating User Performance” and “Evaluating Visualization

Algorithms” scenarios. One area in which scalability evaluation is

well-established is the HPC/visualization community, where the

main focus is on algorithmic scalability with well-deﬁned metrics

and deﬁnitions (e.g., strong scalability). However, the rest of the

visualization community may not be familiar with these deﬁnitions,

and it remains unclear if they could be applied in a broader context

than those with HPC resources.

2.3 Scalability in HCI, Psychology, and Vision Science

Scalability related to humans is different from scalability in

computer science. In their seminal book, Card et al. [14] describe

the human as a processor with numerous capabilities, some of them

ruled by laws or models expressible mathematically. Visualization

is concerned with several of these capabilities, in particular regard-

ing perceptual scalability, cognitive scalability, and movement. The

psychology laws and models often refer to information theory,

considering perception and action as communication through

capacity-limited channels.

SCALABILITY IN VISUALIZATION 3

Scalability has been studied for some aspects of visual percep-

tion, such as ensemble coding [15], preattentive processing [16],

and the limit of the number of colors perceived efﬁciently [17],

Fitts’ law [18] for pointing, the scalability of item selection and

navigation [19], Hick’s Law [20] for reading items, and the

scalability of menus [21]. Budiu [22] discusses several issues

related to scaling user interfaces: working memory limits, screen

size that limits the capacity of the communication channel, and

attention limits. Brown et al. [23] list scalability challenges in

HCI relative to the number of users, the different contexts of use,

and the multiplicity of systems and technologies. Therefore, while

most of the human capabilities exhibit hard limits, interaction

and visualization techniques allow performing tasks with various

interpretations of scalability.

2.4 Summary

Scalability is addressed in many ways by the different disciplines

and communities related to visualization. Still, they share many

concepts but instantiate these concepts with wide variations.

Several articles relate scalability to “factors and certain depen-

dent variables” [9], [12], [24], also called independent variables

and measures. Duboc et al. [9] also mention nuisance variables:

“Variables whose effects cannot be completely controlled for

or variables that are simply not considered in the experiment

design.” They also consider the scalability problem as a multi-

criteria optimization problem with multiple measures to optimize,

combined into a utility function. Although we acknowledge that

their model is useful, we believe it is too complicated with respect

to the interpretations of scalability as seen in the visualization

research community where the measures are not usually combined.

Human capabilities do not scale as nicely as machine ones.

Visual perception is limited in scalability by physiological factors,

such as the number of cones and rods at the lower level. Some

pattern processing allows humans to perform important tasks

efﬁciently (sometimes called “preattentively”), but these perceptual

tasks only work under stringent limits. The eye can track the

movement of a few moving objects on a screen, but this tracking

fails when too many objects cross (visual crowding). Therefore,

scalability-related human performance can hardly be assessed

on theoretical grounds only, it should usually be checked with

experiments. For these reasons, while scalability in the HPC and

distributed computing communities has established deﬁnitions and

evaluation methodologies, these do not directly translate to all parts

of a visualization system with a human in the loop.

In this article, we do not deﬁne scalability but provide a model

to express particular instances of scalability according to the “utility

function” of Duboc et al. [9].

3 SCALABILITY MODEL

Our ﬁrst contribution is a conceptual model that describes the

scalability of a visualization system, component, or technique. The

model is designed to (1) express different scalability concerns that

are relevant to visualization applications (e.g., visual, perceptual,

computational), (2) be applied to different parts of the visualization

pipeline, and (3) allow reasoning about different meanings of

scalable and scalability.

3.1 Model Components

The scalability model represents the scalability of a visualization

process that tackles a speciﬁc problem, by a function with four

components: problem size,resources,assumptions, and effort,

which are described in more detail in the coming subsections.

The function maps the problem size, expected to vary or grow

across applications, to the effort associated with the process’s

solution to the problem, provided an amount of resources and some

assumptions, speciﬁc to the particular problem addressed. The

relationship between these four components is formalized by the

function f:

f:(S;R,A)7−→ E

with

being the set of variables describing the problem size,

describing the available resources,

the assumptions, and

the

effort associated with the result. The components of the conceptual

model are summarized in Figure 1. The notation separates

from

and

to express the difference in role of the actual input

from

the context parameters Rand A.

3.1.1 Problem Sizes S

The problem size variables are properties that characterize the

complexity of the problem targeted or solved by the process. Most

commonly, these variables are descriptions of the size of the input

data: either in number of elements or attributes for discrete data,

or in sample size for continuous data. However, they could also

correspond to data characteristics that go beyond data size, such

as data distribution, or refer to input other than data, such as the

number of simultaneous users or the visual output size (e.g., image

resolution).

3.1.2 Resources R

The resource variables are properties related to the material

components of the system or application environment. They are

factors inﬂuencing effort while being independent of the input data.

They typically include computational resources (e.g., number of

cores, memory), or other resources that the designer can leverage to

improve performance. Resources are characterized by the fact that

they are often limited in practice, and therefore the optimization of

their usage is one lever to improve performance.

In some communities like HPC, being scalable encompasses

the intent to optimize resource usage as well as being designed

to gracefully adapt and make use of any additional resource

available at their maximum capacity. Examples include networks

of computers (e.g., [25]) or grids of projectors (e.g., [26]). In

other communities like HCI, having additional screens is related

to opportunity since screens are relatively cheap and can also be

shared between applications. Scalability questions relate to the

usefulness of dedicating more screens to a visualization application

when the screens are already available (e.g., [27]). Depending on

the community, using multiple processor cores is considered as

resource optimization or opportunity. We connect the resources and

meaning of scalability in more detail in Section 3.2.

problem sizes Sefforts E

resources R

assumptions A

Fig. 1: Conceptual model with problem size variables

and

resource variables

as input, assumptions

, and effort variables

Eas output to f.

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SCALABILITYINVISUALIZATION1ScalabilityinVisualizationGa¨elleRicher,AlexisPister,MoatazAbdelaal,Jean-DanielFekete,MichaelSedlmair,andDanielWeiskopfAbstractWeintroduceaconceptualmodelforscalabilitydesignedforvisualizationresearch.Withthismodel,wesystematicallyanalyzeover120visualizationpublicationsfr...

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