Exponential-time approximation of weighted set cover

Exponential-time approximation of weighted set cover

The Set Cover problem belongs to a group of hard problems which are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. In recent years, many researchers design exact exponential-time algorithms for problems of that kind. The goal is getting the time complexity still of order O(c), but with the co...

Approximation of max independent set, min vertex cover and related problems by moderately exponential algorithms

Using ideas and results from polynomial approximation and exact computation we design approximation algorithms for several NP-hard combinatorial problems achieving ratios that cannot be achieved in polynomial time (unless a very unlikely complexity conjecture is confirmed) with worst-case complexity much lower (though super-polynomial) than that of an exact computation. We study in particular m...

Differential Privacy via Weighted Sampling Set Cover

Differential privacy is a security guarantee model which widely used in privacy preserving data publishing, but the query result can’t be used in data research directly, especially in high-dimensional datasets. To address this problem, we propose a dimensionality reduction method. The core idea of this method is using a series of lowdimensional datasets to reconstruct a high-dimensional dataset...

Weighted geometric set cover problems revisited

We study several set cover problems in low dimensional geometric settings. Specifically, we describe a PTAS for the problem of computing a minimum cover of given points by a set of weighted fat objects. Here, we allow the objects to expand by some prespecified δ-fraction of their diameter. Next, we show that the problem of computing a minimum weight cover of points by weighted halfplanes (witho...

Approximation Algorithms : Set Cover and Max Cut 1 Unweighted Set