This paper studies the problem of maintaining the 2-edge-connected components of a graph undergoing repeated dynamic modifications, such as edge insertions and edge deletions. It is shown how to test at any time whether two vertices belong to the same 2-edge-connected component, and how to insert and delete an edge in $O(m^{2/3} )$ time in the worst case, where m is the current number of edges in the graph.
Galil, Z; Italiano, Giuseppe Francesco. (1992). Fully dynamic algorithms for 2-edge connectivity. SIAM JOURNAL ON COMPUTING, (ISSN: 0097-5397), 21:6, 1047-1069. Doi: 10.1137/0221062.
Fully dynamic algorithms for 2-edge connectivity
Italiano G
1992
Abstract
This paper studies the problem of maintaining the 2-edge-connected components of a graph undergoing repeated dynamic modifications, such as edge insertions and edge deletions. It is shown how to test at any time whether two vertices belong to the same 2-edge-connected component, and how to insert and delete an edge in $O(m^{2/3} )$ time in the worst case, where m is the current number of edges in the graph.
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