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Approximating the Weighted Minimum Label - Cut Problem
In the weighted (minimum) {\sf Label - Cut} problem, we are given a
(directed or undirected) graph , a label set with positive label weights , a source
and a sink . Each edge edge of has a label from .
Different edges may have the same label. The problem asks to find a minimum
weight label subset such that the removal of all edges with labels in
disconnects and .
The unweighted {\sf Label - Cut} problem (i.e., every label has a unit
weight) can be approximated within , where is the number of
vertices of graph . However, it is unknown for a long time how to
approximate the weighted {\sf Label - Cut} problem within . In this
paper, we provide an approximation algorithm for the weighted {\sf Label
- Cut} problem with ratio . The key point of the algorithm is
a mechanism to interpret label weight on an edge as both its length and
capacity.Comment: 21 page