TY - GEN

T1 - Splay Top Trees

AU - Holm, Jacob

AU - Rotenberg, Eva

AU - Ryhl, Alice

PY - 2023

Y1 - 2023

N2 - The top tree data structure is an important and fundamental tool in dynamic graph algorithms. Top trees have existed for decades, and today serve as an ingredient in many state-of-the-art algorithms for dynamic graphs. In this work, we give a new direct proof of the existence of top trees, facilitating simpler and more direct implementations of top trees, based on ideas from splay trees. This result hinges on new insights into the structure of top trees, and in particular the structure of each root path in a top tree. In amortized analysis, our top trees match the asymptotic bounds of the state of the art.

AB - The top tree data structure is an important and fundamental tool in dynamic graph algorithms. Top trees have existed for decades, and today serve as an ingredient in many state-of-the-art algorithms for dynamic graphs. In this work, we give a new direct proof of the existence of top trees, facilitating simpler and more direct implementations of top trees, based on ideas from splay trees. This result hinges on new insights into the structure of top trees, and in particular the structure of each root path in a top tree. In amortized analysis, our top trees match the asymptotic bounds of the state of the art.

U2 - 10.1137/1.9781611977585.ch28

DO - 10.1137/1.9781611977585.ch28

M3 - Article in proceedings

SP - 305

EP - 331

BT - Symposium on Simplicity in Algorithms (SOSA)

A2 - Kavitha, Telikepalli

A2 - Mehlhorn, Kurt

PB - Society for Industrial and Applied Mathematics

T2 - 2023 Symposium on Simplicity in Algorithms (SOSA)

Y2 - 23 January 2023 through 25 January 2023

ER -