A GRAPH MANIPULATION SYSTEM

ABSTRACTED FROM E-LEARNING

Susumu Yamasaki and Mariko Sasakura

Department of Computer Science, Okayama University, 3-1-1 Tsushima-Naka, Okayama, Japan

Keywords:

Graph manipulation, e-Learning Abstraction, Knowledge engineering.

Abstract:

In this position paper, we have an outlook on a graph manipulation system applicable to a visual interface of

managing educational courses for an e-Learning system. We paraphrase a process of learning into a scheme of

state-transitions related to graph manipulations. By the scheme, techniques and tools for educational courses

can be abstracted to the treatments of graphs. Thus we construct a methodology of graph manipulations for

a management of educational courses by extending the established graph viewer. We also propose a simple

sketch-based interface to manipulate graphs. We here list up several tools of the sketch-based interface, based

on the algorithm to detect mouse movements for indicating operations of the system.

1 INTRODUCTION

To develop an e-Learning system, there are various

problems, one of which is concerned with creating

and making contents of e-Learning. For contents-

making, we are required to care speciﬁcations of

teachers, where contents-making contains (i) a design

of education courses, (ii) making education materials

and (iii) a course management.

An adaptive management of courses includes in-

teresting aspects of knowledge engineering, since it

is just to manage contents of courses with respect to

learners’ ideas (which may be interactive with teach-

ers). So far a purpose of this position paper is to show

a method regarding the course managements.

As regards the materials to be made for an educa-

tion course, an abstraction from adaptive e-Learning

systems may be reasonable, because: (a) The mate-

rial induces a function from texts to an abstract op-

eration (which is an idea or a notion for education).

An abstract operation is related to others under a sit-

uation, where the situation is an abstract state of a

learner with respect to a given (computing) environ-

ment. (b) From the views of concrete versus abstract

aspects, concrete objects as means are required, while

abstract ones ﬁtting thoughtful manners of users are

demanded, with reference to the notion of situation.

For such an abstraction, we conceive a state-

transition model. We then have problems for course

managements: (i) How can we construct a course? (ii)

What kind of representation is needed as a construc-

tion of courses? (iii) How can we represent objects

as course materials? (iv) What formulation of course

management with human interface can we make?

To have an insight into such problems, a graph

knowledge structure (which may reﬂect the state-

transition model) is available such that its construc-

tion may be implementable techniques. In Section 2,

we present a state-transition model (graph manipula-

tion) regarding self-learning systems. In Section 3,

graph manipulation tools are described, to some ex-

tent, with reference to managing educational courses.

Section 4 brieﬂy suggests a graph manipulation sys-

tem (Sasakura and Yamasaki, 2008) and some pri-

mary results of this paper, compared with relevant

works.

2 ABSTRACTION FROM

E-LEARNING SYSTEM

Adaptive e-Learning Systems

E-Learning systems have become important in higher

education, especially in universities. Many commer-

cial products or open source systems have been devel-

oped, such as Blackboard, WebCT, or Moodle. Gen-

erally speaking, e-Learning systems may consist of

several features like remote education, assistance for

communication between a teacher and students with

e-mails, or bulletin board systems. We have discussed

self-learning systems in which students read materials

466

Yamasaki S. and Sasakura M..

A GRAPH MANIPULATION SYSTEM ABSTRACTED FROM E-LEARNING.

DOI: 10.5220/0003686604660469

In Proceedings of the International Conference on Knowledge Engineering and Ontology Development (KEOD-2011), pages 466-469

ISBN: 978-989-8425-80-5

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

and take examinations by themselves whenever they

want. Teachers provide materials and exercises in ad-

vance, and check results of students at intervals.

An adaptive e-Learning system (Brusilovski et al.,

2004) is one of self-learning systems. It generates

an educational course in accordance with understand-

ing of a student. Since a student can review mate-

rials which he/she does not master at an appropri-

ate time, the decrease of his/her motivation will be

prevented. The problem in adaptive e-Learning sys-

tems is the way how to build a course that suits to

each student. Knolmayer (2003) used a decision mak-

ing method to build a course. Marshall and Metchell

(2004) proposed to use the Capability Maturity Model

and SPICE that are results of research of software en-

gineering. Conlan et al. propose a qualitative model

for adaptive e-Learning (Colan et al., 2002). Conejo

et al. have made a tool to generate exercises automati-

cally (Conejo et al., 2004). Brusilovsky and Maybury

(2002) have proposed to use the Web system to build

an adaptive system.

On the backgrounds of adaptive e-Learning sys-

tems, we see that contents-making of an e-Learning

system consists of three aspects: (i) The ﬁrst one is to

design an educational course. (ii) The second one is

to make educational materials. (iii) The third one is

to arrange the materials in an educational course.

The problems of contents-making are classiﬁed

into: (1) making educational materials (w.r.t. the

second aspect), and (2) arranging materials in educa-

tional courses (w.r.t. the third aspect).

With respect to making educational materials, the

problem is how teachers could make ‘good” materi-

als. About the arrangement of materials, the prob-

lem is how teachers could handle educational materi-

als and construct educational courses. In this paper,

an educational course is regarded as a list of educa-

tional materials which a student may learn, following

the instructions. Because the managing problem may

be related to computing researches, we here present

the managing tools to assist teachers arranging edu-

cational courses.

A Logical Structure Applicable to Educational

Courses

By means of a self-learning system, we may model

operations and situations, where the operations are

abstracted from educational materials, and situations

represent statuses of how students understand. The

situation may be changed, following what materials

are learned by a student. We assume that the transi-

tion of the situation can be known by an object re-

ﬂecting the material, such that we have a scheme ℑ

= (O, Σ, R, Int), where: (i) O is a set of operations.

(ii) Σ is a set of situations. (iii) R ⊆ (Σ× O) × O. (iv)

Int : L× Env → Σ is a mapping such that L is a set of

learners and Env a set of Web-environments.

∗

stands for a set of all ﬁnite operation se-

quences. A sequence of operations in O

∗

is possibly

interpreted as a process of learning.

An interaction is implemented by the function Int,

where we abstract such a function, assuming that a

learner in an (computing) environment has a situa-

tion. On the other hand, a pair of a situation and an

operation is supposedly related to another operation,

by means of the relation R. Such formal deﬁnitions

represent the behaviour to virtually display an inter-

active human interface for the course working of the

e-Learning system which we are now concerned with.

A relation Seq ⊆ O× O is deﬁned:

Seq(o

, o

) ⇔

(i) o

= o

, or

(ii) ∃ σ

, . . . , σ

m+1

∈ Σ, ∃ o

′

, . . . , o

′

∈ O.

R((σ

, o

), o

′

), R((σ

, o

′

), o

′

), . . . ,

R((σ

, o

′

m−1

), o

′

), R((σ

m+1

, o

′

), o

That is, Seq(o

, o

) means that there is a sequence of

operations beginning with o

and ending with o

Owing to solvability of reachability in graph the-

ory, we can have:

Proposition: Given a scheme with a ﬁnite set

of Env and for any learner, it is solvable whether

Seq(o

, o

) holds for any given two operations o

and

As we may be aware of a relation between the

above proposition and graph reachability, this model

may be translated to a graph manipulation, with which

the basis of the proposed system is described in Sec-

tion 4.

3 GRAPH MANIPULATIONS

VIRTUALLY MANAGING

COURSES

Operations for Managing Courses

Considering a close relation between the state-

transition model (as in the previous section) and

the graph structure, we design graph operations, ab-

stracted from the management of educational courses.

A graph consists of nodes and edges. At ﬁrst, we list

up the operations which are needed to create and ma-

nipulate a graph, based on existing graph description

languages and graph drawing tools (Adar, 2006).

We have the operations of three groups: (1) the

operations for changing a structure of a graph, (2) the

A GRAPH MANIPULATION SYSTEM ABSTRACTED FROM E-LEARNING

467

operations to change a view of a graph, and (3) the op-

erations to manipulate a graph drawing system: The

operations of the ﬁrst group change a logical struc-

ture of a graph, the second group’s operations do not

change a logical structure but change an occurrence

of a graph, while the third group’s operations do not

change a graph.

The operations included in the ﬁrst group can

change the structure of a grap: To create/remove a

node, to create/remove an edge, and to change an

edge’s start point or end point.

The second group includes the operations which

change the characteristics of a node or an edge. We

point out seven operations: To movea node, to change

size/color/line style of a node, to add/change a la-

bel of a node, to change colour/style of an edge, to

add/change a label of an edge, to change style/size of

an arrow head of an edge, and to gather edges.

The third group includes four operations which

do not change anything of a graph, but provide use-

ful functions of a graph drawing system: To scale

up/down, to undo/redo, to save/load, and group-

ing/ungrouping nodes and/or edges.

Our motivation comes from educational courses.

To keep it im mind and to construct a manipulation

package, we would examine a separation of the ma-

nipulation stage for educational courses from the cre-

ating one for educational courses.

For a creation of educational courses, teachers

must make the contents. In a mechanized system,

“creating a node” requires to create new contents for

the node. So far, “creating a node” operation and rel-

ative operations are omitted here from our graph ma-

nipulating system. We will provide another interface

to create a node.

As a result, the operations of the present system

are (a) the operations to change a structure of a graph

except “creating a node”, and (b) the operations for a

system except “grouping/ungrouping” and “changing

views”.

Therefore, we design an interactive system which

provides 8 operations: (1) Moving a node, (2) Moving

an edge (Changing an edge’s start or end point), (3)

Deleting a node, (4) Deleting an edge, (5) Adding an

edge, (6) Undoing, (7) Redoing, and (8) Scaling up.

A graph is loaded, when the system is invoked.

Saving a graph is performed automatically while the

system is running.

A Visual Representation of the Operations

For selected 8 operations of manipulating educational

courses, we can design a simpler system without com-

plicated menus and buttons. Instead of menus or but-

tons, we detect special mouse movements of 8 opera-

Table 1: Visual commands of the system.

Representations Names Operations

Click Scaling up

Line Moving

Crossing lines Deleting

Arrow Drawing

CCW circle Undoing

CW circle Redoing

tions.

As the “ mouse”-device movements, we can de-

tect: click, drawing a line, drawing a crossing lines,

drawing an arrow, drawing a circle by clockwise, and

drawing a circle by counter-clockwise.

Interpreting the movements as the situation de-

mands, we can implement the 8 operations in the

present system. The visual representation of the oper-

ations are shown in Table 1.

We deﬁne Element which is a set of atoms (atomic

visual representations). Element is

{Click, Line, CCWcircle, CWcircle, Node, Edge},

where Click is represented by a “dot”, CCWcircle

and CWcircle are circles with clockwise and counter-

clockwise rotations, respectively. Node and Edge are

elements of a graph.

We deﬁne the visual representations of our in-

terface: Visual representation = Element

, where

Element

is a nonempty set of elements constructed

by at least one atom.

4 A GRAPH MANIPULATION

SYSTEM

The system contains graph manipulations described

in Section 3. We have developed a system which

manipulates graphs for course management (Sasakura

and Yamasaki, 2008).

We have presented a part graph of a course for the

KEOD 2011 - International Conference on Knowledge Engineering and Ontology Development

468

programming language ML (Ullman, 1994). The lay-

out of this graph is designed by the dot program which

is a layout program for directed graphs. The nodes in-

dicate educational materials. They are separated by

4 colors. At the same time, the lines are to point

out some directions. The arrows indicate the order

of learning. The crossing red lines are user’s inputs

which specify the deletion of a node. The red CCW

circle speciﬁes “Undoing” operation to the graph.

So far, we proposed a simple sketch-based inter-

face for materials of an e-Learning system. Using

the interface, we can select commands for manag-

ing a tree by surveying existence of graph editors and

considering characteristics of materials of adaptive e-

Learning systems. We then described how users spec-

ify the commands by mouse movements. Introducing

two predicates which describe the relation of plural

strokes of a mouse, we can specify a command as

multi-stroke drawing. We also mentioned algorithms

to implement the proposed simple sketch-based inter-

face.

As a primary result of this position paper based

on the system (Sasakura and Yamasaki, 2008), we

have presented tools of graph manipulations by which

a whole system has been developed with human in-

terface. As above mentioned, we make an analy-

sis on the e-Learning system in terms of (i) course

designs, (ii) making education materials, and (iii) a

course management. To organize a course manage-

ment, we see the process of self-learning by means of

state-transitions which can be represented by graph

manipulations containing 8 operations as in Section

3. They are closely related to knowledge engineer-

ing, from the views of knowledge structure as well as

ontology developments.

By the system of this paper, we have provided

sketch-based interface not to create a graph but to ma-

nipulate graphs. Our contribution to graph manipula-

tions would easily implement an intuitive interface for

graph manipulations by making use of sketch-based

interface.

Before our approaches, there have been relevant

works, as we have before met: Herman at al. make

a survey on many graph visualization and navigation

techniques in information visualization (Herman et

al., 2000). Freire and Rodriguez (2004) present a

graph-based direct manipulation interface and main-

tain complex hypermedia structure with well-known

graph drawings and visualization techniques. GUESS

(Adar, 2006) is a system for graph exploration.

The interface used in our proposed system is one

of sketch-based interfaces, while sketch-based inter-

faces are often used for drawing some diagrams,

such as Uniﬁed Modeling Language (UML) diagrams

which are included in a popular visual modeling lan-

guage for software engineering. Many UML ed-

itors with sketched-based interface have been pro-

posed (Chen et al., 2008).

In early times, sketch-based interface systems

used Rubine’s algorithm (Rubine, 1991) which recog-

nizes symbols drawn by a single stroke. Recently, to

recognize complicated symbols, multi-stroke recog-

nition systems were proposed (Hse et al., 2004).

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