TY - GEN
T1 - Your Rugby Mates Don’t Need to Know Your Colleagues
T2 - 11th International Conference on Algorithms and Complexity, CIAC 2019
AU - Bulteau, Laurent
AU - Grüttemeier, Niels
AU - Komusiewicz, Christian
AU - Sorge, Manuel
N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - Given an undirected graph the NP-hard Strong Triadic Closure (STC) problem asks for a labeling of the edges as weak and strong such that at most k edges are weak and for each induced in G at least one edge is weak. In this work, we study the following generalizations of STC with c different strong edge colors. In Multi-STC an induced may receive two strong labels as long as they are different. In Edge-List Multi-STC and Vertex-List Multi-STC we may additionally restrict the set of permitted colors for each edge of G. We show that, under the ETH, Edge-List Multi-STC and Vertex-List Multi-STC cannot be solved in time, and that Multi-STC is NP-hard for every fixed c. We then extend previous fixed-parameter tractability results and kernelizations for STC to the three variants with multiple edge colors or outline the limits of such an extension.
AB - Given an undirected graph the NP-hard Strong Triadic Closure (STC) problem asks for a labeling of the edges as weak and strong such that at most k edges are weak and for each induced in G at least one edge is weak. In this work, we study the following generalizations of STC with c different strong edge colors. In Multi-STC an induced may receive two strong labels as long as they are different. In Edge-List Multi-STC and Vertex-List Multi-STC we may additionally restrict the set of permitted colors for each edge of G. We show that, under the ETH, Edge-List Multi-STC and Vertex-List Multi-STC cannot be solved in time, and that Multi-STC is NP-hard for every fixed c. We then extend previous fixed-parameter tractability results and kernelizations for STC to the three variants with multiple edge colors or outline the limits of such an extension.
UR - https://www.scopus.com/pages/publications/85066882318
U2 - 10.1007/978-3-030-17402-6_9
DO - 10.1007/978-3-030-17402-6_9
M3 - Conference contribution
AN - SCOPUS:85066882318
SN - 9783030174019
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 99
EP - 111
BT - Algorithms and Complexity - 11th International Conference, CIAC 2019, Proceedings
A2 - Heggernes, Pinar
PB - Springer Verlag
Y2 - 27 May 2019 through 29 May 2019
ER -