License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2013.461
URN: urn:nbn:de:0030-drops-43936
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2013/4393/
Khodamoradi, Kamyar ;
Krishnamurti, Ramesh ;
Rafiey, Arash ;
Stamoulis, Georgios
PTAS for Ordered Instances of Resource Allocation Problems
Abstract
We consider the problem of fair allocation of indivisible goods where
we are given a set I of m indivisible resources (items) and a set P of n customers (players) competing for the resources. Each resource
j in I has a same value vj > 0 for a subset of customers interested in j and it has no value for other customers. The goal is to find a feasible allocation of the resources to the interested customers such that in the Max-Min scenario (also known as Santa Claus problem) the minimum utility (sum of the resources) received by each of the customers is as high as possible and in the Min-Max case (also known as R||C_max problem), the maximum utility is as low as possible.
In this paper we are interested in instances of the problem that admit a PTAS. These instances are not only of theoretical interest but also have practical applications. For the Max-Min allocation problem, we start with instances of the problem that can be viewed as a convex bipartite graph; there exists an ordering of the resources such that each customer is interested (has positive evaluation) in a set of consecutive resources and we demonstrate a PTAS. For the Min-Max allocation problem, we obtain a PTAS for instances in which there is an ordering of the customers (machines) and each resource (job) is adjacent to a consecutive set of customers (machines).
Next we show that our method for the Max-Min scenario, can be extended to a broader class of bipartite graphs where the resources can be viewed as a tree and each customer is interested in a sub-tree of a bounded number of leaves of this tree (e.g. a sub-path).
BibTeX - Entry
@InProceedings{khodamoradi_et_al:LIPIcs:2013:4393,
author = {Kamyar Khodamoradi and Ramesh Krishnamurti and Arash Rafiey and Georgios Stamoulis},
title = {{PTAS for Ordered Instances of Resource Allocation Problems}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)},
pages = {461--473},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-64-4},
ISSN = {1868-8969},
year = {2013},
volume = {24},
editor = {Anil Seth and Nisheeth K. Vishnoi},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2013/4393},
URN = {urn:nbn:de:0030-drops-43936},
doi = {10.4230/LIPIcs.FSTTCS.2013.461},
annote = {Keywords: Approximation Algorithms, Convex Bipartite Graphs, Resource Allocation}
}
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Keywords: |
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Approximation Algorithms, Convex Bipartite Graphs, Resource Allocation |
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Collection: |
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IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013) |
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Issue Date: |
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2013 |
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Date of publication: |
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10.12.2013 |
