SHERP

Approximability of the k-Server Disconnection Problem

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Authors
Hong, Sung-Pil; Choi, Byung-Cheon
Issue Date
2007-09-04
Publisher
Wiley-Blackwell
Citation
Networks 50(2007), 273-282
Keywords
server–network disconnection; inapproximability; approximation algorithm; fixed-parameter cases
Description
The definitive version is available at www3.interscience.wiley.com.
Abstract
Consider a network of k servers and their users. Each server provides a unique service that has a certain utility for each user. Now comes an attacker who wishes to destroy a set of network edges to maximize his net gain, namely the total disconnected utilities of the users minus the total edge-destruction cost. This k -server disconnection problem is NP-hard and, furthermore, cannot be approximated within a polynomially computable factor of the optimumwhen k is part of the input. Even for any fixed k ≥ 2, there is a constant > 0 such that approximation of the problem within a factor 1/(1 + ) of the optimum is NP-hard. However, a 12 + 1 2k+1−2 -approximation can be created in the time of O(2k ) applications of a min-cut algorithm. The main idea is to approximate the optimum with special solutions computable in polynomial time due to supermodularity. Therefore, when the the network has, as is usual in most cases, only a few servers, a 0.5-approximation can be carried out in polynomial time.
ISSN
0028-3045
Language
English
URI
http://hdl.handle.net/10371/5349
DOI
https://doi.org/10.1002/net.20203
https://doi.org/10.1002/net.20203
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Appears in Collections:
College of Engineering/Engineering Practice School (공과대학/대학원)Dept. of Industrial Engineering (산업공학과)Journal Papers (저널논문_산업공학과)
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