# A Simple Greedy Algorithm for Dynamic Graph Orientation

## Edvin Berglin and Gerth Stølting Brodal

In Proc. 28th Annual International Symposium on Algorithms and Computation, volume 92 of Leibniz International Proceedings in Informatics, 12:1-12:12 pages. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Dagstuhl Publishing, Germany, 2017.

## Abstract

Graph orientations with low out-degree are one of several ways to efficiently store sparse graphs. If the graphs allow for insertion and deletion of edges, one may have to flip the orientation of some edges to prevent blowing up the maximum out-degree. We use arboricity as our sparsity measure. With an immensely simple greedy algorithm, we get parametrized trade-off bounds between out-degree and worst case number of flips, which previously only existed for amortized number of flips. We match the previous best worst-case algorithm (in O(log n) flips) for general arboricity and beat it for either constant or super-logarithmic arboricity. We also match a previous best amortized result for at least logarithmic arboricity, and give the first results with worst-case O(1) and O(\sqrt{log n}) flips nearly matching degree bounds to their respective amortized solutions.

Online version

isaac17.pdf (513 Kb)

DOI

10.4230/LIPIcs.ISAAC.2017.12

BIBTEX entry

@incollection{isaac17,
author = "Edvin Berglin and Gerth St{\o}lting Brodal",
booktitle = "Proc. 28th Annual International Symposium on Algorithms and Computation",
doi = "10.4230/LIPIcs.ISAAC.2017.12",
isbn = "978-3-95977-054-5",
pages = "12:1-12:12",
publisher = "Schloss Dagstuhl - Leibniz-Zentrum f\"ur Informatik, Dagstuhl Publishing, Germany",
series = "Leibniz International Proceedings in Informatics",
title = "A Simple Greedy Algorithm for Dynamic Graph Orientation",
volume = "92",
year = "2017"
}