NDLI: Load Balancing in Quorum Systems

Please wait, while we are loading the content...

Load Balancing in Quorum Systems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Marcus, Yosi Peleg, David Holzman, Ron
Copyright Year	1997
Abstract	This paper introduces and studies the question of balancing the load on processors participating in a given quorum system. Our proposed measure for the degree of balancing is the ratio between the load on the least frequently referenced element and on the most frequently used one.We give some simple sufficient and necessary conditions for perfect balancing. We then look at the balancing properties of the common class of voting systems and prove that every voting system with odd total weight is perfectly balanced. (This holds, in fact, for the more general class of ordered systems.)We also give some characterizations for the balancing ratio in the worst case. It is shown that for any quorum system with a universe of size n, the balancing ratio is no smaller than $1/(n-1)$, and this bound is the best possible. When restricting attention to nondominated coteries (NDCs), the bound becomes $2/\bigl(n-\log_2 n+o(\log n)\bigr)$, and there exists an NDC with ratio $2/\bigl(n-\log_2 n-o(\log n)\bigr)$.Next, we study the interrelations between the two basic parameters of load balancing and quorum size. It turns out that the two size parameters suitable for our investigation are the size of the largest quorum and the optimally weighted average quorum size(OWAQS) of the system. For the class of ordered NDCs (for which perfect balancing is guaranteed), it is shown that over a universe of size n, some quorums of size $\lceil(n+1)/2\rceil$ or more must exist (and this bound is the best possible). A similar lower bound holds for the OWAQS measure if we restrict attention to voting systems. For nonordered systems, perfect balancing can sometimes be achieved with much smaller quorums. A lower bound of $\Omega(\sqrt{n})$ is established for the maximal quorum size and the OWAQS of any perfectly balanced quorum system over n elements, and this bound is the best possible.Finally, we turn to quorum systems that cannot be perfectly balanced, but have some balancing ratio $0 < \rho < 1$. For such systems we study the trade-offs between the required balancing ratio $\rho$ and the quorum size it admits in the best case. It is easy to get an analogue of the result for perfect balancing, yielding a lower bound of $\sqrt{n\rho}$. We actually get a better estimate by a refinement of the argument.
Starting Page	223
Ending Page	245
Page Count	23
File Format	PDF
ISSN	08954801
DOI	10.1137/S0895480193260303
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	2
Volume Number	10
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-01
Access Restriction	Subscribed
Subject Keyword	load balancing coterie quorum intersecting hypergraphs Network design and communication Hypergraphs Combinatorics
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
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

The Load and Availability of Byzantine Quorum Systems

The Load, Capacity, and Availability of Quorum Systems

Coloring 2-intersecting hypergraphs

Covers in Partitioned Intersecting Hypergraphs

Matching criticality in intersecting hypergraphs

Shattered matchings in intersecting hypergraphs

On Ryser's Conjecture for Linear Intersecting Multipartite Hypergraphs

Most Probably Intersecting Hypergraphs

Non-intersecting Ryser hypergraphs

Load Balancing in Quorum Systems

Similar Documents

The Load and Availability of Byzantine Quorum Systems

The Load, Capacity, and Availability of Quorum Systems

Coloring 2-intersecting hypergraphs

Covers in Partitioned Intersecting Hypergraphs

Matching criticality in intersecting hypergraphs

Shattered matchings in intersecting hypergraphs

On Ryser's Conjecture for Linear Intersecting Multipartite Hypergraphs

Most Probably Intersecting Hypergraphs

Non-intersecting Ryser hypergraphs

Load Balancing in Quorum Systems