eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-12-06
41:1
41:13
10.4230/LIPIcs.ISAAC.2018.41
article
Approximation Algorithms for Facial Cycles in Planar Embeddings
Da Lozzo, Giordano
1
https://orcid.org/0000-0003-2396-5174
Rutter, Ignaz
2
https://orcid.org/0000-0002-3794-4406
Computer Science Department, Roma Tre University, Italy
Department of Computer Science and Mathematics, University of Passau, Germany
Consider the following combinatorial problem: Given a planar graph G and a set of simple cycles C in G, find a planar embedding E of G such that the number of cycles in C that bound a face in E is maximized. This problem, called Max Facial C-Cycles, was first studied by Mutzel and Weiskircher [IPCO '99, http://dx.doi.org/10.1007/3-540-48777-8_27) and then proved NP-hard by Woeginger [Oper. Res. Lett., 2002, http://dx.doi.org/10.1016/S0167-6377(02)00119-0].
We establish a tight border of tractability for Max Facial C-Cycles in biconnected planar graphs by giving conditions under which the problem is NP-hard and showing that strengthening any of these conditions makes the problem polynomial-time solvable. Our main results are approximation algorithms for Max Facial C-Cycles. Namely, we give a 2-approximation for series-parallel graphs and a (4+epsilon)-approximation for biconnected planar graphs. Remarkably, this provides one of the first approximation algorithms for constrained embedding problems.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol123-isaac2018/LIPIcs.ISAAC.2018.41/LIPIcs.ISAAC.2018.41.pdf
Planar Embeddings
Facial Cycles
Complexity
Approximation Algorithms