TY - GEN

T1 - Simple deterministic algorithms for fully dynamic maximal matching

AU - Neiman, Ofer

AU - Solomon, Shay

PY - 2013

Y1 - 2013

N2 - A maximal matching can be maintained in fully dynamic (supporting both addition and deletion of edges) n-vertex graphs using a trivial deterministic algorithm with a worstcase update time of On). No deterministic algorithm that outperforms the näive O(n) one was reported up to this date. The only progress in this direction is due to Ivkovíc and Lloyd [14], who in 1993 devised a deterministic algorithm with an amortized update time of O((n+m) √ 2/2), where m is the number of edges. In this paper we show the first deterministic fully dynamic algorithm that outperforms the trivial one. Specifically, we provide a deterministic worst-case update time of O( √ m). Moreover, our algorithm maintains a matching which is in fact a 3/2-approximate maximum cardinality matching (MCM). We remark that no fully dynamic algorithm for maintaining (2-ε)-approximate MCM improving upon the näive O(n) was known prior to this work, even allowing amortized time bounds and randomization. For low arboricity graphs (e.g., planar graphs and graphs excluding fixed minors), we devise another simple deterministic algorithm with sub-logarithmic update time. Specifically, it maintains a fully dynamic maximal matching with amortized update time of O(log n/ log log n). This result addresses an open question of Onak and Rubinfeld [19]. We also show a deterministic algorithm with optimal space usage of O(n + m), that for arbitrary graphs maintains a maximal matching with amortized update time of O( √ m).

AB - A maximal matching can be maintained in fully dynamic (supporting both addition and deletion of edges) n-vertex graphs using a trivial deterministic algorithm with a worstcase update time of On). No deterministic algorithm that outperforms the näive O(n) one was reported up to this date. The only progress in this direction is due to Ivkovíc and Lloyd [14], who in 1993 devised a deterministic algorithm with an amortized update time of O((n+m) √ 2/2), where m is the number of edges. In this paper we show the first deterministic fully dynamic algorithm that outperforms the trivial one. Specifically, we provide a deterministic worst-case update time of O( √ m). Moreover, our algorithm maintains a matching which is in fact a 3/2-approximate maximum cardinality matching (MCM). We remark that no fully dynamic algorithm for maintaining (2-ε)-approximate MCM improving upon the näive O(n) was known prior to this work, even allowing amortized time bounds and randomization. For low arboricity graphs (e.g., planar graphs and graphs excluding fixed minors), we devise another simple deterministic algorithm with sub-logarithmic update time. Specifically, it maintains a fully dynamic maximal matching with amortized update time of O(log n/ log log n). This result addresses an open question of Onak and Rubinfeld [19]. We also show a deterministic algorithm with optimal space usage of O(n + m), that for arbitrary graphs maintains a maximal matching with amortized update time of O( √ m).

KW - Dynamic algorithms

KW - Maximal matching

KW - Maximum matching

UR - http://www.scopus.com/inward/record.url?scp=84879800829&partnerID=8YFLogxK

U2 - 10.1145/2488608.2488703

DO - 10.1145/2488608.2488703

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:84879800829

SN - 9781450320290

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 745

EP - 753

BT - STOC 2013 - Proceedings of the 2013 ACM Symposium on Theory of Computing

T2 - 45th Annual ACM Symposium on Theory of Computing, STOC 2013

Y2 - 1 June 2013 through 4 June 2013

ER -