NDLI: Tight Bounds for Online Vector Scheduling

Content Provider	IEEE Xplore Digital Library
Author	Sungjin Im Kell, N. Kulkarni, J. Panigrahi, D.
Copyright Year	2015
Description	Author affiliation: Dept. of Comput. Sci., Duke Univ., Durham, NC, USA (Kell, N.; Panigrahi, D.) \|\| Electr. Eng. & Comput. Sci., Univ. of California at Merced, Merced, CA, USA (Sungjin Im) \|\| Microsoft Res., Redmond, WA, USA (Kulkarni, J.)
Abstract	Modern data centers face a key challenge of effectively serving user requests that arrive online. Such requests are inherently multi-dimensional and characterized by demand vectors over multiple resources such as processor cycles, storage space, and network bandwidth. Typically, different resources require different objectives to be optimized, and $L_{r}$ norms of loads are among the most popular objectives considered. Furthermore, the server clusters are also often heterogeneous making the scheduling problem more challenging. To address these problems, we consider the online vector scheduling problem in this paper. Introduced by Chekuri and Khanna (SIAM J. of Comp. 2006), vector scheduling is a generalization of classical load balancing, where every job has a vector load instead of a scalar load. The scalar problem, introduced by Graham in 1966, and its many variants (identical and unrelated machines, makespan and $L_{r}-norm$ optimization, offline and online jobs, etc.) have been extensively studied over the last 50 years. In this paper, we resolve the online complexity of the vector scheduling problem and its important generalizations - for all $L_{r}$ norms and in both the identical and unrelated machines settings. Our main results are: · For identical machines, we show that the optimal competitive ratio is Θ(log d/ log log d) by giving an online lower bound and an algorithm with an asymptotically matching competitive ratio. The lower bound is technically challenging, and is obtained via an online lower bound for the minimum mono-chromatic clique problem using a novel online coloring game and randomized coding scheme. Our techniques also extend to asymptotically tight upper and lower bounds for general $L_{r}$ norms. · For unrelated machines, we show that the optimal competitive ratio is Θ(log m + log d) by giving an online lower bound that matches a previously known upper bound. Unlike identical machines, however, extending these results, particularly the upper bound, to general $L_{r}$ norms requires new ideas. In particular, we use a carefully constructed potential function that balances the individual $L_{r}$ objectives with the overall (convexified) min-max objective to guide the online algorithm and track the changes in potential to bound the competitive ratio.
Starting Page	525
Ending Page	544
File Size	420547
Page Count	20
File Format	PDF
ISBN	9781467381918
ISSN	02725428
DOI	10.1109/FOCS.2015.39
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-10-17
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Approximation methods Load management Processor scheduling Upper bound Color Computer science Electronic mail load balancing Online algorithms scheduling
Content Type	Text
Resource Type	Article

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