Assessing the Computational Complexity of Multi-layer Subgraph Detection
Multi-layer graphs consist of several graphs (layers) over the same vertex set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the border of computational (in)tractability for the class of subgraph detection problems on multi-layer graphs, including fundamental problems such as maximum matching, finding certain clique relaxations (motivated by community detection), or path problems. Mostly encountering hardness results, sometimes even for two or three layers, we can also spot some islands of tractability.
KeywordsDirected Acyclic Graph Hamiltonian Path Graph Property Hereditary Property Vertex Subset
HM and MS were supported by the DFG, project DAPA (NI 369/12). CK was supported by the DFG, project MAGZ (KO 3669/4–1). RB was partially supported by the DFG, fellowship BR 5207/2. This work was initiated at the research retreat of the TU Berlin Algorithmics and Computational Complexity group held in Darlingerode, Harz mountains, in April 2014.
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