Orienting fully dynamic graphs with worst-case time bounds

Tsvi Kopelowitz, Robert Krauthgamer, Ely Porat, Shay Solomon

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

35 Scopus citations


In edge orientations, the goal is usually to orient (direct) the edges of an undirected network (modeled by a graph) such that all out-degrees are bounded. When the network is fully dynamic, i.e., admits edge insertions and deletions, we wish to maintain such an orientation while keeping a tab on the update time. Low out-degree orientations turned out to be a surprisingly useful tool for managing networks. Brodal and Fagerberg (1999) initiated the study of the edge orientation problem in terms of the graph's arboricity, which is very natural in this context. Their solution achieves a constant out-degree and a logarithmic amortized update time for all graphs with constant arboricity, which include all planar and excluded-minor graphs. It remained an open question - first proposed by Brodal and Fagerberg, later by Erickson and others - to obtain similar bounds with worst-case update time. We address this 15 year old question by providing a simple algorithm with worst-case bounds that nearly match the previous amortized bounds. Our algorithm is based on a new approach of maintaining a combinatorial invariant, and achieves a logarithmic out-degree with logarithmic worst-case update times. This result has applications to various dynamic network problems such as maintaining a maximal matching, where we obtain logarithmic worst-case update time compared to a similar amortized update time of Neiman and Solomon (2013).

Original languageEnglish
Title of host publicationAutomata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings
PublisherSpringer Verlag
Number of pages12
EditionPART 2
ISBN (Print)9783662439500
StatePublished - 2014
Event41st International Colloquium on Automata, Languages, and Programming, ICALP 2014 - Copenhagen, Denmark
Duration: 8 Jul 201411 Jul 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 2
Volume8573 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference41st International Colloquium on Automata, Languages, and Programming, ICALP 2014


Dive into the research topics of 'Orienting fully dynamic graphs with worst-case time bounds'. Together they form a unique fingerprint.

Cite this