Approximation algorithm for weighted set cover, using multiplicative weights
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05-11-2019 - |
题
It is known that the problem of fractional set cover
can be rephrased as a linear programming problem and be approximated using the multiplicative weights method, for instance this lecture note shows how to do so.
The running time depends on the "width" of the problem, which equals to the number of sets in the unweighted case. However, in the weighted case, the width of the problem depends on the weight function, hence the running time is exponential with respect to the representation of the problem. Is there a way to overcome this issue? Either a way to reduce it to polynomial running time or proof that it's impossible (under plausible complexity assumptions)?
没有正确的解决方案
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