In addition to the mathematical and empirical analyses of algorithms, there is yet a third way to study algorithms. It is called algorithm visualization and can be defined as the use of images to convey some useful information about algorithms.

**Algorithm
Visualization**

In
addition to the mathematical and empirical analyses of algorithms, there is yet
a third way to study algorithms. It is called ** algorithm visualization**
and can be defined as the use of images to convey some useful information about
algorithms. That information can be a visual illustration of an algorithm’s
operation, of its per-formance on different kinds of inputs, or of its
execution speed versus that of other algorithms for the same problem. To
accomplish this goal, an algorithm visualiza-tion uses graphic elements—points,
line segments, two- or three-dimensional bars, and so on—to represent some
“interesting events” in the algorithm’s operation.

There are
two principal variations of algorithm visualization:

Static algorithm visualization

Dynamic algorithm visualization, also called algorithm animation

Static algorithm visualization shows an algorithm’s progress through a series of still images. Algorithm animation, on the other hand, shows a continuous, movie-like presentation of an algorithm’s operations. Animation is an arguably more sophisticated option, which, of course, is much more difficult to implement.

Early
efforts in the area of algorithm visualization go back to the 1970s. The
watershed event happened in 1981 with the appearance of a 30-minute color sound
film titled *Sorting Out Sorting*. This
algorithm visualization classic was produced at the University of Toronto by
Ronald Baecker with the assistance of D. Sherman [Bae81, Bae98]. It contained
visualizations of nine well-known sorting algorithms (more than half of them
are discussed later in the book) and provided quite a convincing demonstration
of their relative speeds.

The
success of *Sorting Out Sorting* made
sorting algorithms a perennial fa-vorite for algorithm animation. Indeed, the
sorting problem lends itself quite naturally to visual presentation via
vertical or horizontal bars or sticks of different heights or lengths, which
need to be rearranged according to their sizes (Figure 2.8). This presentation
is convenient, however, only for illustrating actions of a typical sorting
algorithm on small inputs. For larger files, *Sorting Out Sorting* used the ingenious idea of presenting data by a
scatterplot of points on a coordinate plane, with the first coordinate
representing an item’s position in the file and the second one representing the
item’s value; with such a representation, the process of sorting looks like a
transformation of a “random” scatterplot of points into the points along a
frame’s diagonal (Figure 2.9). In addition, most sorting algorithms

work by
comparing and exchanging two given items at a time—an event that can be
animated relatively easily.

Since the
appearance of *Sorting Out Sorting*, a
great number of algorithm animations have been created, especially after the
appearance of Java and the

World
Wide Web in the 1990s. They range in scope from one particular algorithm to a
group of algorithms for the same problem (e.g., sorting) or the same
applica-tion area (e.g., geometric algorithms) to general-purpose animation
systems. At the end of 2010, a catalog of links to existing visualizations,
maintained under the NSF-supported AlgoVizProject, contained over 500 links.
Unfortunately, a survey of existing visualizations found most of them to be of
low quality, with the content heavily skewed toward easier topics such as
sorting [Sha07].

There are
two principal applications of algorithm visualization: research and education.
Potential benefits for researchers are based on expectations that algo-rithm
visualization may help uncover some unknown features of algorithms. For
example, one researcher used a visualization of the recursive Tower of Hanoi
algo-rithm in which odd- and even-numbered disks were colored in two different
colors. He noticed that two disks of the same color never came in direct
contact during the algorithm’s execution. This observation helped him in developing
a better non-recursive version of the classic algorithm. To give another
example, Bentley and McIlroy [Ben93] mentioned using an algorithm animation
system in their work on improving a library implementation of a leading sorting
algorithm.

The
application of algorithm visualization to education seeks to help students
learning algorithms. The available evidence of its effectiveness is decisively
mixed. Although some experiments did register positive learning outcomes,
others failed to do so. The increasing body of evidence indicates that creating
sophisticated software systems is not going to be enough. In fact, it appears
that the level of student involvement with visualization might be more
important than specific features of visualization software. In some
experiments, low-tech visualizations prepared by students were more effective
than passive exposure to sophisticated software systems.

To
summarize, although some successes in both research and education have been
reported in the literature, they are not as impressive as one might expect. A
deeper understanding of human perception of images will be required before the
true potential of algorithm visualization is fulfilled.

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Introduction to the Design and Analysis of Algorithms : Fundamentals of the Analysis of Algorithm Efficiency : Algorithm Visualization |

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