Abstract
In the (nonpreemptive) Generalized Min Sum Set Cover Problem, we
are given n ground elements and a collection of sets S = {S_1,
S_2, ..., S_m} where each set S_i in 2^{[n]} has a positive
requirement k(S_i) that has to be fulfilled. We would like to order all elements to minimize the total (weighted) cover time of all sets. The cover time of a set S_i is defined as the first index j in the ordering such that the first j elements in the ordering contain k(S_i) elements in S_i. This problem was introduced by [Azar, Gamzu and Yin, 2009] with interesting motivations in web page ranking and broadcast scheduling. For this problem, constant approximations are known [Bansal, Gupta and Krishnaswamy, 2010][Skutella and Williamson, 2011].
We study the version where preemption is allowed. The difference is
that elements can be fractionally scheduled and a set S is
covered in the moment when k(S) amount of elements in S are scheduled. We give a 2approximation for this preemptive problem. Our linear programming and analysis are completely different from [Bansal, Gupta and Krishnaswamy, 2010][Skutella and Williamson, 2011]. We also show that any preemptive solution can be transformed into a nonpreemptive one by losing a factor of 6.2 in the objective function. As a byproduct, we obtain an improved 12.4approximation for the nonpreemptive problem.
BibTeX  Entry
@InProceedings{im_et_al:LIPIcs:2012:3399,
author = {Sungjin Im and Maxim Sviridenko and Ruben van der Zwaan},
title = {{Preemptive and NonPreemptive Generalized Min Sum Set Cover}},
booktitle = {29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)},
pages = {465476},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783939897354},
ISSN = {18688969},
year = {2012},
volume = {14},
editor = {Christoph D{\"u}rr and Thomas Wilke},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2012/3399},
URN = {urn:nbn:de:0030drops33991},
doi = {10.4230/LIPIcs.STACS.2012.465},
annote = {Keywords: Set Cover, Approximation, Preemption, Latency, Average cover time}
}
Keywords: 

Set Cover, Approximation, Preemption, Latency, Average cover time 
Collection: 

29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012) 
Issue Date: 

2012 
Date of publication: 

24.02.2012 