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+---
+title: Introduction
+description: |
+  Summing up the contents of the „Rank-Balanced Trees“ chapter.
+tags:
+  - balanced trees
+---
+
+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_. We will mainly discuss the implementation of a set.
+
+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 _red-black tree_, as described by _Guibas and_
+_Sedgewick_[^1]. Among other alternatives, we can find (non-binary) _B-tree_[^2]
+and _AVL tree_[^3].
+
+We will start by discussing the properties of the AVL tree[^3], then we will
+follow up on that with a definition of a _rank-balanced tree_, including
+implementation of algorithms for implementing commonly known trees such as red-black
+tree and AVL tree using the given representation. Afterwards we will delve into
+the details of the _Weak AVL (WAVL) tree_[^4] that has relaxed requirements
+compared to the AVL tree.
+
+[^1]: GUIBAS, Leo J.; SEDGEWICK, Robert. A dichromatic framework for balanced trees. In: _19th Annual Symposium on Foundations of Computer Science (sfcs 1978)_. 1978, pp. 8–21. Available from doi: [10.1109/SFCS.1978.3](https://doi.org/10.1109/SFCS.1978.3).
+[^2]: BAYER, R.; MCCREIGHT, E. Organization and Maintenance of Large Ordered Indices. In: _Proceedings of the 1970 ACM SIGFIDET (Now SIGMOD) Workshop on Data Description, Access and Control_. Houston, Texas: Association for Computing Machinery, 1970, pp. 107–141. SIGFIDET ’70. isbn 9781450379410. Available from doi: [10.1145/1734663.1734671](https://doi.org/10.1145/1734663.1734671).
+[^3]: ADELSON-VELSKIJ, Georgij; LANDIS, Evgenij. An algorithm for the organization of information. _Doklady Akad. Nauk SSSR_. 1962, vol. 146, pp. 263–266.
+[^4]: HAEUPLER, Bernhard; SEN, Siddhartha; TARJAN, Robert E. Rank-Balanced Trees. _ACM Trans. Algorithms_. 2015, vol. 11, no. 4. issn 1549-6325. Available from doi: [10.1145/2689412](https://doi.org/10.1145/2689412).
diff --git a/algorithms/99-rank-balanced-trees/_category_.yaml b/algorithms/99-rank-balanced-trees/_category_.yaml
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+label: Rank-Balanced Trees
+position: 99
+link:
+  type: generated-index
+  description: |
+    Web version of my bachelor thesis on rank-balanced trees.