Abstract
The special properties of trees allow us to create algorithms that are specialized for trees and work more efficiently than general graph algorithms. This chapter presents a selection of such algorithms. Section 10.1 introduces basic concepts and algorithms related to trees. A central problem is finding the diameter of a tree, i.e., the maximum distance between two nodes. We will learn two linear time algorithms for solving the problem. Section 10.2 focuses on processing queries on trees. We will learn to use a tree traversal array to process various queries related to subtrees and paths. After this, we will discuss methods for determining lowest common ancestors and an offline algorithm which is based on merging data structures. Section 10.3 presents two advanced tree processing techniques: centroid decomposition and heavy-light decomposition.
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Notes
- 1.
Sleator and Tarjan [29] introduced the idea in the context of their link/cut tree data structure.
- 2.
The notation \(\log ^k n\) corresponds to \((\log n)^k\).
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Laaksonen, A. (2017). Tree Algorithms. In: Guide to Competitive Programming. Undergraduate Topics in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-319-72547-5_10
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DOI: https://doi.org/10.1007/978-3-319-72547-5_10
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