TY - GEN
T1 - Fully dynamic MIS in uniformly sparse graphs
AU - Onak, Krzysztof
AU - Schieber, Baruch
AU - Solomon, Shay
AU - Wein, Nicole
N1 - Publisher Copyright:
© 2018 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.
PY - 2018/7/1
Y1 - 2018/7/1
N2 - We consider the problem of maintaining a maximal independent set (MIS) in a dynamic graph subject to edge insertions and deletions. Recently, Assadi, Onak, Schieber and Solomon (STOC 2018) showed that an MIS can be maintained in sublinear (in the dynamically changing number of edges) amortized update time. In this paper we significantly improve the update time for uniformly sparse graphs. Specifically, for graphs with arboricity α, the amortized update time of our algorithm is O(α2 · log2 n), where n is the number of vertices. For low arboricity graphs, which include, for example, minor-free graphs as well as some classes of “real world” graphs, our update time is polylogarithmic. Our update time improves the result of Assadi et al. for all graphs with arboricity bounded by m3/8−, for any constant > 0. This covers much of the range of possible values for arboricity, as the arboricity of a general graph cannot exceed m1/2.
AB - We consider the problem of maintaining a maximal independent set (MIS) in a dynamic graph subject to edge insertions and deletions. Recently, Assadi, Onak, Schieber and Solomon (STOC 2018) showed that an MIS can be maintained in sublinear (in the dynamically changing number of edges) amortized update time. In this paper we significantly improve the update time for uniformly sparse graphs. Specifically, for graphs with arboricity α, the amortized update time of our algorithm is O(α2 · log2 n), where n is the number of vertices. For low arboricity graphs, which include, for example, minor-free graphs as well as some classes of “real world” graphs, our update time is polylogarithmic. Our update time improves the result of Assadi et al. for all graphs with arboricity bounded by m3/8−, for any constant > 0. This covers much of the range of possible values for arboricity, as the arboricity of a general graph cannot exceed m1/2.
KW - Dynamic graph algorithms
KW - Graph arboricity
KW - Independent set
KW - Sparse graphs
UR - http://www.scopus.com/inward/record.url?scp=85049778875&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85049778875&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ICALP.2018.92
DO - 10.4230/LIPIcs.ICALP.2018.92
M3 - Conference contribution
AN - SCOPUS:85049778875
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018
A2 - Kaklamanis, Christos
A2 - Marx, Daniel
A2 - Chatzigiannakis, Ioannis
A2 - Sannella, Donald
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018
Y2 - 9 July 2018 through 13 July 2018
ER -