Slides used by Kausal in his presentation in the third International Conference on Recent Trends in Information Technology (ICRTIT 2013) in MIT, Chennai on 25th July.

1. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
Cake Cutting of CPU Resources among multiple
HPC agents on a Cloud
Kausal Malladi, Debargha Ganguly
International Institute of Information Technology - Bangalore
July 25, 2013
Kausal Malladi, Debargha Ganguly Paper ID: 158 ICRTIT 2013 1/26

2. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
Agenda
1 Introduction
2 Existing Algorithms
3 Proposed Algorithm
4 Performance
5 Conclusion
6 References
Kausal Malladi, Debargha Ganguly Paper ID: 158 ICRTIT 2013 2/26

3. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
Quick Introduction
Cloud Computing
Cloud computing is a model for enabling ubiquitous, convenient,
on-demand network access to a shared pool of configurable
computing resources (e.g., networks, servers, storage, applications,
and services) that can be rapidly provisioned and released with
minimal management effort or service provider interaction
Resource
A resource is any physical or virtual component of limited
availability within a computer system
Shared resource
A shared resource is a piece of information on a computer that can
be remotely accessed from another computer, typically via a LAN
or an enterprise Intranet
Kausal Malladi, Debargha Ganguly Paper ID: 158 ICRTIT 2013 3/26

4. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
Quick Introduction
Cake Cutting
Fair division is the problem of dividing a set of goods between
several people, such that each person receives his/her due share.
This problem arises in various real-world settings: auctions, divorce
settlements, electronic spectrum and frequency allocation, airport
traffic management, or exploitation of Earth Observation Satellites
High Performance Agents
A supercomputer is a computer at the frontline of contemporary
processing capacity, particularly speed of calculation
Game Theory
Game theory is a study of strategic decision making. More
formally, it is the study of mathematical models of conflict and
cooperation between intelligent rational decision makers
Kausal Malladi, Debargha Ganguly Paper ID: 158 ICRTIT 2013 4/26

5. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
Quick Introduction
Problem Statement
Cake Cutting of resources (CPU) among several dynamically
adding HPC agents on a Cloud, ensuring that the resources are
utilized to the utmost.
Kausal Malladi, Debargha Ganguly Paper ID: 158 ICRTIT 2013 5/26

6. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
Existing Algorithms
Dominant Resource Fairness (DRF) Algorithm, proposed by
Ghodsi et. al.
Dynamic Dominant Resource Fairness (Dynamic DRF)
Algorithm, proposed by Kash et. al.
Max-min Algorithm, proposed by Kumar et. al.
Assumptions
Agents once added don’t leave the system
Agents demand resources in fixed proportions
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7. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
Dominant Resource Fairness (DRF) Algorithm
Sharing Incentive
Each user should be better off sharing the cluster, than exclusively
using her own partition of the cluster. Consider a cluster with
identical nodes and n users. Then a user should not be able to
allocate more tasks in a cluster partition consisting of 1/n of all
resources
Strategy-proofness
Users should not be able to benefit by lying about their resource
demands. This provides incentive compatibility, as a user cannot
improve her allocation by lying
Kausal Malladi, Debargha Ganguly Paper ID: 158 ICRTIT 2013 7/26

8. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
Dominant Resource Fairness (DRF) Algorithm
Envy-freeness
A user should not prefer the allocation of another user. This
property embodies the notion of fairness
Pareto efficiency
It should not be possible to increase the allocation of a user
without decreasing the allocation of at least another user. This
property is important as it leads to maximizing system utilization
subject to satisfying the other properties
Kausal Malladi, Debargha Ganguly Paper ID: 158 ICRTIT 2013 8/26

9. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
Dominant Resource Fairness (DRF) Algorithm
Static resource allocation
Meets all four properties of a fair allocation policy
For every user, computes the share of each resource allocated
Maximum among all shares is the dominant share
Corresponding resource is called dominant resource
Kausal Malladi, Debargha Ganguly Paper ID: 158 ICRTIT 2013 9/26

10. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
Dynamic DRF Algorithm
Strategyproofness
No agent can misreport its demand vector and be strictly better off
at any step k, regardless of the reported demands of other agents
Dynamic Pareto Optimality
At each step the allocation should not be Pareto dominated by any
other allocation that only redistributes the collective entitlements
of the agents present in the system among those agents
Kausal Malladi, Debargha Ganguly Paper ID: 158 ICRTIT 2013 10/26

11. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
Dynamic DRF Algorithm
Sharing Incentive
When an agent arrives it receives an allocation that it likes at least
as much as an equal split of the resources. This models a setting
where agents have made equal contributions to the system and
hence have equal entitlements
Dynamic Envy Freeness
At any step an agent i envies an agent j only if j arrived before i
did and j has not been allocated any resources since i arrived
Kausal Malladi, Debargha Ganguly Paper ID: 158 ICRTIT 2013 11/26

12. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
Dynamic DRF Algorithm
Works for a dynamic setting
Satisfies all the four properties and can be implemented in
polynomial time
HPC agents?
Single resource type?
Kausal Malladi, Debargha Ganguly Paper ID: 158 ICRTIT 2013 12/26

13. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
Max-min Algorithm
Maximum of minimum amount of resources that can be
allocated to a host
Assigns weights to agents
Each agent receives allocation proportional to its weight
Static setting, proved to satisfy four properties of DRF
Algorithm
Dynamic setting?
Kausal Malladi, Debargha Ganguly Paper ID: 158 ICRTIT 2013 13/26

14. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
Features
Inspired from Dynamic DRF Algorithm
Linear Program (LP) formulation
HPC agents
Dynamic setting
Assumptions
Only a certain number of agents can be run on a host
Agents follow Game-Theoretic approach in demanding
Agents once added won’t leave host
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15. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
The Algorithm
Algorithm 1: Modified Dynamic DRF Planner
1 agentCount ← 1;
2 foreach new agent added do
3 if agentCount ≤ maxAgentsthen
4 d[agentCount] ← demand by new agent;
5 proportion ← solve LP(agentCount,d);
6 for i=1 toagentCount do
7 allocation[i] ← proportion[i]∗d[i]/agentCount;
8 i←i+1;
9 end
10 end
11 agentCount ← agentCount+1;
12 end
Kausal Malladi, Debargha Ganguly Paper ID: 158 ICRTIT 2013 15/26

16. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
The Algorithm...continued
Algorithm 2: solve LP(agentCount,d)
Data: N ← total resource units available on host machine
Result: proportion [i]
1 Maximize S such that
2 proportion[i][k]≥ S
3 proportion[i][k]≥ proportion[i − 1][k]
4
N
k=1 proportion[i][k]*d[k] ≤ i/N
Kausal Malladi, Debargha Ganguly Paper ID: 158 ICRTIT 2013 16/26

17. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
Results
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18. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
Results
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19. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
Results
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20. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
Results
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21. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
Results - Summary
Kausal Malladi, Debargha Ganguly Paper ID: 158 ICRTIT 2013 21/26

22. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
Winding it up...
Proposed Algorithm works in the dynamic setting
Works well for Computationally intensive HPC agents
Performs better than traditionally implemented algorithms
Assumptions are realistic and do not lead to loss of generality
Resources utilized to the utmost!
Future Work
Performance optimization
Less number of assumptions
Kausal Malladi, Debargha Ganguly Paper ID: 158 ICRTIT 2013 22/26

23. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
Acknowledgement
Prof. Dr. Shrisha Rao, IIITB
Continuous help in terms of showcasing results effectively and
suggestions to make the proposed algorithm better
Testers
Anshul Sharma
Pakalapati Srinivas Raju
Pratibind Jha
Kausal Malladi, Debargha Ganguly Paper ID: 158 ICRTIT 2013 23/26

24. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
References
Peter Mell and Tim Grance, “The NIST Definition of Cloud
Computing,” 2009
A. D. Procaccia, “Cake cutting: Not just child’s play,” in
Communications of the ACM, 2013
C. Vecchiola, S. Pandey and R. Buyya, “High Performance
Cloud Computing: A view of Scientific Applications,”in
Proceedings of the 2009 10th International Symposium on
pervasive Systems, Algorithms and Networks, ISPAN ’09,
(Washington, USA), pp 4-16, IEEE Computer Society, 2009
S. Tijs and T. Driessen, “Game Theory and cost allocation
Problems,” tech. rep., 1986
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25. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
References...continued
A. Ghodsi, M. Zaharia, B. Hindman, A. Konwinski, S. Shenker
and I. Stoica, “Dominant Resource Fairness: Fair Allocation
of Multiple Resource Types,” in Proceedings of the 8th
USENIX conference on Networked Systems design and
implementation, NSDI 11, (Berkeley, CA, USA), pp. 24-24,
USENIX Association, 2011
I. Kash, A. D. Procaccia and N. Shah, “No Agent Left Behind:
Dynamic Fair Division of Multiple Resources,” in Proceedings
of the 11th International Conference on Autonomous Agents
and Multi-Agent Systems, AA-MAS, 2013
P. Kumar, A. Verma, “Independent Task Scheduling in Cloud
Computing by Improved Genetic Algorithm,” in International
Journal of Advanced Research in Computer Science and
Software Engineering, vol. 2, issue 5, pp. 111-114, May 2012
Kausal Malladi, Debargha Ganguly Paper ID: 158 ICRTIT 2013 25/26

26. Agenda Introduction Existing Algorithms Proposed Algorithm Performance Conclusion References
Thank you!
{kausalmalladi, debargha.ganguly}@gmail.com
http://www.kausalmalladi.tk
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