10 lines
1.8 KiB
TeX
10 lines
1.8 KiB
TeX
\chapter*{Introduction}
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\addcontentsline{toc}{chapter}{Introduction}
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Data structures have become a regular part of the essential toolbox for problem-solving. In many cases, they also help to improve the existing algorithm's performance, e.g. using a priority queue in Dijkstra's algorithm for the shortest path. This thesis will mainly discuss the implementation of a set.
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Currently, the most commonly used implementations of sets use hash tables, but we will talk about another common alternative, implementation via self-balancing search trees. Compared to a hash table, they provide consistent time complexity, but at the cost of a requirement for ordering on the elements. The most implemented self-balancing binary tree is a \textit{red-black tree}, as described by Guibas and Sedgewick~\cite{rbtree}. Among other alternatives, we can find (non-binary) \textit{B-tree}~\cite{btree} and \textit{AVL tree}~\cite{avl}.
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This thesis analyses and visualizes the \textit{Weak AVL (WAVL)}\cite{wavl} tree that has more relaxed conditions than the AVL tree, but still provides better balancing than a red-black tree.
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We start by reiterating through commonly used search trees, explaining basic ideas behind their self-balancing and bounding the height in the worst-case scenario. Then we state used terminology and explain the rank-balanced tree. Given a rank-balanced tree, we can delve into the details behind the representation of previously shown self-balancing binary search trees using rank and the WAVL rule gives us a new self-balancing binary search tree. For the WAVL, we provide pseudocode and explain operations used for rebalancing, including diagrams. Later on, we will discuss different heuristics that can be used for rebalancing and implementing the visualization of the operations on the WAVL tree.
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