NDLI: On Centralized Smooth Scheduling

Content Provider	Springer Nature Link
Author	Litman, Ami Moran Schein, Shiri
Copyright Year	2009
Abstract	This paper studies evenly distributed sets of natural numbers and their applications to scheduling in a centralized environment. Such sets, called smooth sets, have the property that their quantity within each interval is proportional to the size of the interval, up to a bounded additive deviation; namely, for ρ,Δ∈ℝ a set A of natural numbers is (ρ,Δ)-smooth if abs(\|I\|⋅ρ−\|I∩A\|)<Δ for any interval I⊂ℕ.The paper studies scheduling persistent clients on a single slot-oriented resource in a flexible and predictable manner. Each client γ has a given rate ρ γ that defines the share of the resource he is entitled to receive and the goal is a smooth schedule in which, for some predefined Δ, each client γ is served in a (ρ γ,Δ)-smooth set of slots (natural numbers).The paper considers a centralized environment where a single algorithm computes the user of the current slot. It constructs a smooth schedule with a very efficient algorithm that computes the user of each slot in O(log log q) time and O(n) space, where n is the number of clients and q ≜max {ρ γ/ρ γ′ \| γ,γ′∈Γ}; in many practical applications this O(log log q) value is actually a small constant.Our scheduling technique is based on a reduction from allocation of slots to allocation of sub-intervals of the unit interval. This technique naturally extends to the problem of scheduling multiple resources, even under the restriction that a client can be served concurrently by at most one resource. This paper constructs such a schedule in which the users of each slot are computed very fast—in O(mlog log q) time per slot and O(n) space where m is the number of resources; this result is a significant improvement on the prior fastest algorithm that produces such a schedule (actually of a special type—a P-fair schedule) in O(mlog n) time per slot and O(n) space.Moreover, the paper introduces a novel approach to multi-resource scheduling in which each resource independently computes, slot after slot, what client to serve in this slot. Under this approach the paper constructs a smooth schedule which is computed in O(n) space and O(log log q) time per slot.
Starting Page	464
Ending Page	480
Page Count	17
File Format	PDF
ISSN	01784617
Journal	Algorithmica
Volume Number	60
Issue Number	2
e-ISSN	14320541
Language	English
Publisher	Springer-Verlag
Publisher Date	2009-09-11
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Data Structures, Cryptology and Information Theory Computer Systems Organization and Communication Networks Algorithm Analysis and Problem Complexity Mathematics of Computing Theory of Computation Algorithms
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Science Applications

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
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
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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