Abstract
We study the problem of maintaining the 2-edge-, 2-vertex-, and 3-edge-connected components of a dynamic planar graph subject to edge deletions. The 2-edge-connected components can be maintained in a total of O(n log n) time under any sequence of at most O(n) deletions. This gives O(log n) amortized time per deletion. The 2-vertex- and 3-edge-connected components can be maintained in a total of O(n log2 n) time. This gives O(log2 n) amortized time per deletion. The space required by all our data structures is O(n).
Research partially supported by the ESPRIT II Basic Research Actions Program of the EC under Project ALCOM (contract No. 3075) and Project ASMICS. Work done while the first author was visiting Columbia University, partially supported by a CNR Fellowship and the second author was on leave from Università di Roma, Italy.
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Giammarresi, D., Italiano, G.F. (1992). Dynamic 2- and 3-connectivity on planar graphs. In: Nurmi, O., Ukkonen, E. (eds) Algorithm Theory — SWAT '92. SWAT 1992. Lecture Notes in Computer Science, vol 621. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55706-7_19
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DOI: https://doi.org/10.1007/3-540-55706-7_19
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