Commit e9ac7079 by Ondřej Mička

### Graphs: Minor changes

parent ae8844c7
 ... ... @@ -185,14 +185,13 @@ time. \section[linkcut]{Link-cut trees} Link-cut trees are dynamic version of the heavy-light decomposition. They allow us to change structure of the represented forest by either linking two trees or by cutting an edge inside a tree. Link-cut trees were introduced in a paper by Sleator and Tarjan \TODO reference. However, we will show later version that uses splay trees instead of original biased binary trees \TODO reference. Although it achieves the time complexity only in amortized case, it is significantly easier to analyze. edge inside a tree. Link-cut trees were introduced in a paper by Sleator and Tarjan in 1982. However, we will show later version from 1985, also by Sleator and Tarjan, that uses splay trees instead of original biased binary trees. Although it achieves the time complexity only in amortized case, it is significantly easier to analyze. Link-cut tree represents a forest $F$ of \em{rooted} trees; each edge is oriented towards the respective root. It supports following operations: \TODO proper formatting \list{o} \: Structural queries: \tightlist{-} ... ... @@ -258,9 +257,8 @@ we jump to the top of the newly created fat path and repeat the whole process. \figure[expose-idea]{expose-idea.pdf}{}{One step of $\Expose$ in the thin-fat decomposition.} \theorem{ \theoremn{Sleator, Tarjan'82}{ $\Expose$ operation performs $\O(\log n)$ steps amortized. \TODO reference S\&T'82 } By using a balanced binary tree to represent fat paths, we obtain ... ...
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