Abstract
Given an undirected graph G=(V,E) 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 P3 in G at least one edge is weak. We study the following generalizations of STC with c different strong edge colors. In Multi-STC an induced P3 may receive two strong labels as long as they are different. In Edge-List Multi-STC and Vertex-List Multi-STC we may restrict the set of permitted colors for each edge of G. We show that, under the Exponential Time Hypothesis (ETH), Edge-List Multi-STC and Vertex-List Multi-STC cannot be solved in time 2o(|V|2). We proceed with a parameterized complexity analysis in which we extend previous algorithms and kernelizations for STC [11,14] to the three variants or outline the limits of such an extension.
Original language | English |
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Pages (from-to) | 75-96 |
Number of pages | 22 |
Journal | Journal of Computer and System Sciences |
Volume | 120 |
DOIs | |
State | Published - 1 Sep 2021 |
Externally published | Yes |
Keywords
- Edge coloring
- Exponential time hypothesis
- Fixed-parameter tractability
- Kernelization
- Social network analysis
ASJC Scopus subject areas
- Theoretical Computer Science
- General Computer Science
- Computer Networks and Communications
- Computational Theory and Mathematics
- Applied Mathematics