\section{Introduction}
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% Fragestellung & Zielsetzung - aim & research objectives
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% Vorgehensweise
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% Why important, who participants, trends, 


Simplification of polygonal data structures is the task of reducing data points while preserving topological characteristics. The simplification often takes the form of removing points that make up the geometry. There are several solutions that tackle the problem in different ways. With the rising trend of moving desktop applications to the web platform geographic information systems have experienced the shift towards web browsers too \parencite{alesheikh2002web}. Performance is critical in these applications. Since simplification is an important factor to performance the solutions will be tested by constructing a web application using a technology called WebAssembly. 


\subsection{Binary instruction sets on the web platform}

The recent development of WebAssembly allows code written in various programming languages to be run natively in web browsers. So far JavaScript was the only native programming language on the web \parencite{reiser2017accelerate}. The goals of WebAssembly are to define a binary instruction format as a compilation target to execute code at native speed and taking advantage of common hardware capabilities \parencite{haas2017bringing}. The integration into the web platform brings portability to a wide range of platforms like mobile and internet of things. The usage of this technology promises performance gains that will be tested by this thesis. The results can give conclusions to whether WebAssembly is worth a consideration for web applications with geographic computational aspects. WebGIS is only one technology that would benefit greatly of such an advancement. Thus far WebAssembly has been shipped to the stable version of the four most used browser engines \parencite{wagner2017support}. The mainly targeted high-level languages for compilation are C and C++. Also a compiler for Rust and a TypeScript subset has been developed.

\subsection{Performance as important factor for web applications}

There has been a rapid growth of complex applications running in web-browsers. These so called progressive web apps combine the fast reachability of web pages with the feature richness of locally installed applications. Even though these applications can grow quite complex, the requirement for fast page loads and instant user interaction still remains. One way to cope with this need is the use of compression algorithms to reduce the amount of data transmitted and processed. In a way simplification is a form of data compression. Web servers use lossless compression algorithms like gzip to deflate data before transmission. Browsers that implement these algorithms can then fully restore the requested ressources resulting in lower bandwidth usage. The algorithms presented here however remove information from the data in a way that cannot be restored. This is called lossy compression. The most common usage for this on the web is the compression of image data. 

\subsection{Topology simplification for rendering performance}

While compression is often used to minimize bandwidth usage, the compression of geospatial data can particulary influence rendering performance. The bottleneck for rendering often is the transformation to scalable vector graphics used to display topology on the web. Implementing simplification algorithms for use on the web platform can lead to smoother user experience when working with large geodata sets. 

\subsection{Related work}
There have been previous attempts to speed up applications with WebAssembly. They all have seen great performance benefits when using this technology. Results show that over several source languages the performance is predictably consistent across browsers \parencite{surma2019replacing}. Reiser and Bläser even propose to cross-compile JavaScript to WebAssembly. Through their developed library Speedy.js one can compile TypeScript, a JavaScript superset, to WebAssembly. The performance gains of critical functions reaches up to a factor of four \parencite{reiser2017accelerate}.

Shi and Cheung analyzed several different polyline simplification algorithms in 2006 regarding their performance and quality \parencite{shi2006performance}. In this thesis the algorithms will also be introduced. The performance benchmarking however will be limited to only the most effective algorithm that is used on the web. 

\subsection{Structure of this thesis}

This thesis is structured into a theoretical and a practical component. First the theoretical principles will be reviewed. A number of algorithms will be introduced in this section. Each algorithm will be dissected by complexity and characteristics. Topology of polygonal data will be explained as how to describe geodata on the web. An introduction to WebAssembly will follow.

In chapter 3 the practical implementation will be presented. A web application will be developed to measure the performance of three related algorithms used for polyline simplification.

The results of the above methods will be shown in chapter 4. After discussion of the results a conclusion will finish the thesis.

