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Client-Server Assignment for Internet Distributed Systems
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Overview
• Introduction• Problem Definition• Problem Model• Solution• Conclusion
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IntroductionInternet - Distributed System Example: Email,IMS
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Features:1. Communication Load Clients assigned to two different servers. Clients assigned to same server.
2. Load Balancing Use fewer servers. Servers are heavily loaded
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Observations:
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Problem Definition
Optimal client server assignment for a pre-specified trade-off between load balance and communication load.
Emerging Applications:1. Social networks Eg: Facebook
2. Distributed database system, Eg: MapReduce
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Communication Model
Initially assign clients to a system with 2 servers (Sa, Sb)
Then we extend the 2-server solution to multiple servers.
Xi = 1, client i is assigned to SaXi = -1, client i is assigned to Sb : data rate from client i to client j.
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Communication Load if i and j are assigned to same server. 2 if clients are assigned to 2 different servers.
Total communication load,
If i and j are assigned to different servers, = -1
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Load Balance
Load balance, D =
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D can be expressed as, Refer link
Adding D to objective function will make the function non-quadratic.
Hence we modify D,
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Equivalent formula of D, D = , where Refer link
As, = 1,= Refer link
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Optimization problem:
Minimize:
Subject to :
Where:
=
is an arbitrary co-efficient (0≤ ≤1)
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Objective function : minimize
Where we define,
Refer link
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Semidefinite Programming Semidefinite programming is a class of convex
optimization. : set of real Symmetric matrices. A matrix is called positive semidefinite if ,
for all It satisfies strict quadratic programming
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Solution: minimize: tr( subject to: Solution Matrix =
W-> Matrix with diagonal elements 0 and Wi,jU -> symmetric & Positive semidefinite matrix
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Conclusion
1. Hard problems could be formulated as a optimization problem and solved.
2. optimization problems, are widely used in tremendous number of application areas, such as transportation, production planning, logistics etc.
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Presented by : Swathi Balakrishna
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Extra information:Transform program into Vector program:
Minimize:
Subject to: = 1,
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Vector programming -> Semidefinite programming
W-> Matrix with diagonal elements 0 and Wi,jU -> symmetric & Positive semidefinite matrix minimize: tr( subject to:
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Solution Matrix = Cholesky Factorization: Obtain V= ( Satisfying .
Final solution:Round n vectors (to n integers (