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

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 itsel...

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Vydáno v:Theoretical computer science Ročník 648; s. 72 - 83
Hlavní autoři: Zhang, Peng, Fu, Bin
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 04.10.2016
Témata:
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
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Shrnutí: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.
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ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2016.08.006