TY - GEN

T1 - Decremental maintenance of strongly connected components

AU - Roditty, Liam

PY - 2013

Y1 - 2013

N2 - We consider the problem of maintaining the strongly connected components (SCCs) of an n-nodes and m-edges directed graph that undergoes a sequence of edge deletions. Recently, in SODA 2011, Ła̧cki presented a deterministic algorithm that preprocess the graph in O(mn) time and creates a data structure that maintains the SCCs of a graph under edge deletions with a total update time of O(mn). The data structure answers strong connectivity queries in O(1) time. The worst case update time after a single edge deletion might be as large as O(mn). In this paper we reduce the preprocessing time and the worst case update time of Ła̧cki's data structure from O(mn) to O(m log n). The query time and the total update time remain unchanged.

AB - We consider the problem of maintaining the strongly connected components (SCCs) of an n-nodes and m-edges directed graph that undergoes a sequence of edge deletions. Recently, in SODA 2011, Ła̧cki presented a deterministic algorithm that preprocess the graph in O(mn) time and creates a data structure that maintains the SCCs of a graph under edge deletions with a total update time of O(mn). The data structure answers strong connectivity queries in O(1) time. The worst case update time after a single edge deletion might be as large as O(mn). In this paper we reduce the preprocessing time and the worst case update time of Ła̧cki's data structure from O(mn) to O(m log n). The query time and the total update time remain unchanged.

UR - http://www.scopus.com/inward/record.url?scp=84876052364&partnerID=8YFLogxK

U2 - 10.1137/1.9781611973105.82

DO - 10.1137/1.9781611973105.82

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AN - SCOPUS:84876052364

SN - 9781611972511

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 1143

EP - 1150

BT - Proceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013

PB - Association for Computing Machinery

T2 - 24th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013

Y2 - 6 January 2013 through 8 January 2013

ER -