Incremental edge orientation in forests

Michael A. Bender, Tsvi Kopelowitz, William Kuszmaul, Ely Porat, Clifford Stein

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations


For any forest G = (V, E) it is possible to orient the edges E so that no vertex in V has out-degree greater than 1. This paper considers the incremental edge-orientation problem, in which the edges E arrive over time and the algorithm must maintain a low-out-degree edge orientation at all times. We give an algorithm that maintains a maximum out-degree of 3 while flipping at most O(log log n) edge orientations per edge insertion, with high probability in n. The algorithm requires worst-case time O(log n log log n) per insertion, and takes amortized time O(1). The previous state of the art required up to O(log n/log log n) edge flips per insertion. We then apply our edge-orientation results to the problem of dynamic Cuckoo hashing. The problem of designing simple families H of hash functions that are compatible with Cuckoo hashing has received extensive attention. These families H are known to satisfy static guarantees, but do not come typically with dynamic guarantees for the running time of inserts and deletes. We show how to transform static guarantees (for 1-associativity) into near-state-of-the-art dynamic guarantees (for O(1)-associativity) in a black-box fashion. Rather than relying on the family H to supply randomness, as in past work, we instead rely on randomness within our table-maintenance algorithm.

Original languageEnglish
Title of host publication29th Annual European Symposium on Algorithms, ESA 2021
EditorsPetra Mutzel, Rasmus Pagh, Grzegorz Herman
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772044
StatePublished - 1 Sep 2021
Event29th Annual European Symposium on Algorithms, ESA 2021 - Vitual, Lisbon, Portugal
Duration: 6 Sep 20218 Sep 2021

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference29th Annual European Symposium on Algorithms, ESA 2021
CityVitual, Lisbon

Bibliographical note

Publisher Copyright:
© Michael A. Bender, Tsvi Kopelowitz, William Kuszmaul, Ely Porat, and Clifford Stein; licensed under Creative Commons License CC-BY 4.0


  • Cuckoo hashing
  • Edge orientation
  • Graph algorithms
  • Hash functions


Dive into the research topics of 'Incremental edge orientation in forests'. Together they form a unique fingerprint.

Cite this