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Worst-Case Polylog Incremental SPQR-trees: Embeddings, Planarity, and Triconnectivity [article]

Jacob Holm, Eva Rotenberg
2019 arXiv   pre-print
Using this, we obtain deterministic data structures for incremental planarity testing, incremental planar embedding, and incremental triconnectivity, that each have worst case O(log^3 n) update and query  ...  Our proof is based on BC trees and SPQR trees, and we develop pre-split variants of these for general graphs, based on a novel biased heavy-path decomposition, where the structural changes corresponding  ...  As a consequence, we obtain an algorithm for incremental planarity testing of a biconnected graph with worst-case polylog update time (see Section 7.5).  ... 
arXiv:1910.09005v1 fatcat:x6l7vkgujjhsrbg5hoagswp564