Link-Cut Trees support dynamic tree operations. Core Operations: - Link: Connect two trees - Cut: Disconnect edge - Path queries: Aggregate on root-to-node path Key Concept: Preferred paths decompose tree.
Splay trees represent preferred paths. Access Operation: Makes path to root preferred.
All other operations build on access. Applications: - Dynamic connectivity - Online LCA queries - Path aggregates in changing trees Time: amortized. Space: .