The label cut problem with respect to path length and label frequency

• Published in: Theoretical computer science Vol. 648; pp. 72 - 83
• Main Authors: Zhang, Peng, Fu, Bin
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 04.10.2016
• Subjects: Algorithms; Approximation algorithm; Computational complexity; Constants; Disengaging; Global Label Cut; Graph theory; Graphs; Label [formula omitted] Cut; Labels; Parameterized algorithm; Parameters; Polynomials; Label s-t Cut; Global Label Cut; Parameterized algorithm; Approximation algorithm; Computational complexity
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/j.tcs.2016.08.006

Given a graph with labels defined on edges and a source-sink pair (s,t), the Labels-tCut problem asks for a minimum number of labels such that the removal of edges with these labels disconnects s and t. Similarly, the Global Label Cut problem asks for a minimum number of labels to disconnect G itself. For these two problems, we identify two useful parameters, i.e., lmax, the maximum length of any s-t path (only applies to Labels-tCut), and fmax, the maximum number of appearances of any label in the graph (applies to the two problems). We show that lmax=2 and fmax=2 are two complexity thresholds for Labels-tCut. Furthermore, we give (i) an O⁎(ck) time parameterized algorithm for Labels-tCut with lmax bounded from above, where parameter k is the number of labels in a solution, and c is a constant with lmax−1<c<lmax, (ii) a combinatorial lmax-approximation algorithm for Labels-tCut, and (iii) a polynomial time exact algorithm for Global Label Cut with fmax bounded from above. •We give an FPT algorithm for Labels-tCut in a special case.•We give a pure combinatorial approximation algorithm for Labels-tCut.•We give a polynomial time exact algorithm for Global Label Cut in a special case.