NDLI: Admission control to minimize rejections and online set cover with repetitions

Content Provider	ACM Digital Library
Author	Gutner, Shai Alon, Noga Azar, Yossi
Copyright Year	2009
Abstract	We study the admission control problem in general networks. Communication requests arrive over time, and the online algorithm accepts or rejects each request while maintaining the capacity limitations of the network. The admission control problem has been usually analyzed as a benefit problem, where the goal is to devise an online algorithm that accepts the maximum number of requests possible. The problem with this objective function is that even algorithms with optimal competitive ratios may reject almost all of the requests, when it would have been possible to reject only a few. This could be inappropriate for settings in which rejections are intended to be rare events. In this article, we consider preemptive online algorithms whose goal is to minimize the number of rejected requests. Each request arrives together with the path it should be routed on. We show an $O(log^{2}$ $(\textit{mc}))-competitive$ randomized algorithm for the weighted case, where $\textit{m}$ is the number of edges in the graph and $\textit{c}$ is the maximum edge capacity. For the unweighted case, we give an $\textit{O}(log$ $\textit{m}$ log $\textit{c})-competitive$ randomized algorithm. This settles an open question of Blum et al. [2001]. We note that allowing preemption and handling requests with given paths are essential for avoiding trivial lower bounds. The admission control problem is a generalization of the online set cover with repetitions problem, whose input is a family of $\textit{m}$ subsets of a ground set of $\textit{n}$ elements. Elements of the ground set are given to the online algorithm one by one, possibly requesting each element a multiple number of times. (If each element arrives at most once, this corresponds to the online set cover problem.) The algorithm must cover each element by different subsets, according to the number of times it has been requested. We give an $\textit{O}(log$ $\textit{m}$ log $\textit{n})-competitive$ randomized algorithm for the online set cover with repetitions problem. This matches a recent lower bound of Ω(log $\textit{m}$ log $\textit{n})$ given by Korman [2005] (based on Feige [1998]) for the competitive ratio of any randomized $\textit{polynomial}$ time algorithm, under the $\textit{BPP}$ ≠ $\textit{NP}$ assumption. Given any constant &epsis; > 0, an $\textit{O}(log$ $\textit{m}$ log $\textit{n})-competitive$ deterministic bicriteria algorithm is shown that covers each element by at least (1 ™ $&epsis;)\textit{k}$ sets, where $\textit{k}$ is the number of times the element is covered by the optimal solution.
Starting Page	1
Ending Page	13
Page Count	13
File Format	PDF
ISSN	15496325
e-ISSN	15496333
DOI	10.1145/1644015.1644026
Volume Number	6
Issue Number	1
Journal	ACM Transactions on Algorithms (TALG)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2009-12-28
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Admission control Competitive Online Set cover
Content Type	Text
Resource Type	Article
Subject	Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
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8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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