[{"citation":{"mla":"Strothmann, Willy-Bernhard, and Tamás Lukovszki. Decremental Biconnectivity on Planar Graphs. 1997.","bibtex":"@book{Strothmann_Lukovszki_1997, place={Paderborn}, title={Decremental Biconnectivity on Planar Graphs}, author={Strothmann, Willy-Bernhard and Lukovszki, Tamás}, year={1997} }","chicago":"Strothmann, Willy-Bernhard, and Tamás Lukovszki. Decremental Biconnectivity on Planar Graphs. Paderborn, 1997.","ama":"Strothmann W-B, Lukovszki T. Decremental Biconnectivity on Planar Graphs. Paderborn; 1997.","apa":"Strothmann, W.-B., & Lukovszki, T. (1997). Decremental Biconnectivity on Planar Graphs. Paderborn.","ieee":"W.-B. Strothmann and T. Lukovszki, Decremental Biconnectivity on Planar Graphs. Paderborn, 1997.","short":"W.-B. Strothmann, T. Lukovszki, Decremental Biconnectivity on Planar Graphs, Paderborn, 1997."},"year":"1997","type":"report","language":[{"iso":"eng"}],"_id":"18955","date_updated":"2022-01-06T06:53:55Z","department":[{"_id":"63"}],"file_date_updated":"2020-09-03T12:59:44Z","author":[{"full_name":"Strothmann, Willy-Bernhard","first_name":"Willy-Bernhard","last_name":"Strothmann"},{"last_name":"Lukovszki","first_name":"Tamás","full_name":"Lukovszki, Tamás"}],"file":[{"file_name":"pub-hni-901.pdf","date_created":"2020-09-03T12:59:44Z","access_level":"closed","file_size":222106,"creator":"koala","file_id":"18957","date_updated":"2020-09-03T12:59:44Z","content_type":"application/pdf","success":1,"relation":"main_file"}],"date_created":"2020-09-03T12:59:56Z","has_accepted_license":"1","status":"public","abstract":[{"lang":"eng","text":"In this paper we present a (randomized) algorithm for maintaining the biconnected components of a dynamic planar graph of $n$ vertices under deletions of edges. The biconnected components can be maintained under any sequence of edge deletions in a total of $O(n log n)$ time, with high probability. This gives $O(log n)$ amortized time per edge deletion, which improves previous (deterministic) results due to Giammarresi and Italiano, where $O(n log^2 n)$ amortized time is needed. Our work describes a simplification of the data structures from [GiIt96] and uses dynamic perfect hashing to reduce the running time. As in the paper by Giammarresi and Italiano, we only need $O(n)$ space. Finally we describe some simply additional operations on the decremental data structure. By aid of them this the data structure is applicable for finding efficiently a $Delta$-spanning tree in a biconnected planar graph with a maximum degree $2Delta-2$ do to Czumaj and Strothmann."}],"place":"Paderborn","title":"Decremental Biconnectivity on Planar Graphs","ddc":["000"],"user_id":"15415"}]