Golovach, Petr A.
[Author];
Requilé, Clément
[Author];
Thilikos, Dimitrios M.
[Author]
;
Petr A. Golovach and Clément Requilé and Dimitrios M. Thilikos
[Contributor]
Footnote:
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Description:
The Plane Diameter Completion problem asks, given a plane graph G and a positive integer d, if it is a spanning subgraph of a plane graph H that has diameter at most d. We examine two variants of this problem where the input comes with another parameter k. In the first variant, called BPDC, k upper bounds the total number of edges to be added and in the second, called BFPDC, k upper bounds the number of additional edges per face. We prove that both problems are NP-complete, the first even for 3-connected graphs of face-degree at most 4 and the second even when k=1 on 3-connected graphs of face-degree at most 5. In this paper we give parameterized algorithms for both problems that run in O(n^{3})+2^{2^{O((kd)^2\log d)}} * n steps.