TY - GEN

T1 - Variants of plane diameter completion

AU - Golovach, Petr A.

AU - Requilé, Clément

AU - Thilikos, Dimitrios M.

N1 - Publisher Copyright:
© Petr A. Golovach, Clément Requilé, and Dimitrios M. Thilikos;.

PY - 2015/11/1

Y1 - 2015/11/1

N2 - 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 κ. In the first variant, called BPDC, κ upper bounds the total number of edges to be added and in the second, called BFPDC, κ 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 κ = 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(n3) + 22O((κd)2 log d) · n steps.

AB - 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 κ. In the first variant, called BPDC, κ upper bounds the total number of edges to be added and in the second, called BFPDC, κ 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 κ = 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(n3) + 22O((κd)2 log d) · n steps.

KW - Branchwidth

KW - Dynamic programming

KW - Graph modification problems

KW - Parameterized algorithms

KW - Planar graphs

UR - http://www.scopus.com/inward/record.url?scp=84958243326&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84958243326&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.IPEC.2015.30

DO - 10.4230/LIPIcs.IPEC.2015.30

M3 - Conference contribution

AN - SCOPUS:84958243326

T3 - Leibniz International Proceedings in Informatics, LIPIcs

SP - 30

EP - 42

BT - 10th International Symposium on Parameterized and Exact Computation, IPEC 2015

A2 - Husfeldt, Thore

A2 - Husfeldt, Thore

A2 - Kanj, Iyad

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 10th International Symposium on Parameterized and Exact Computation, IPEC 2015

Y2 - 16 September 2015 through 18 September 2015

ER -