Constructing Efficient Overlays

• Problem formulation– Given a set of

subscribers and a set of machines, distributed in the Internet

– Construct an overlay tree to minimize the traffic/latency from the event source to the subscribers

Constructing Efficient Overlays (Cont.)

• Model 1– Subscribers cannot relay traffic– Restricted steiner tree– Developed a new approximation algorithm

with a factor of 4.1

• Model 2 (p2p)– Subscribers can relay traffic– Minimum steiner tree problem– Apply existing approximation algorithms

Load Balancing• Given a set of machines• Machine i can handle

Di rectangles as a dispatcher or Si rectangles as a server

• Problem:– Which set of machines are

servers, and which set of machines aredispatcher?

– How to assign server machines to dispatcher machines?

• Objective function min(max sj/Sj or dj/Dj)

events

D D D

S S S S S

Four Variations of the Problem

• Configured or not– Whether each machine is already configured to be a

dispatcher or a server

• Unique or not– Whether each server can only be assigned to a

unique dispatcher or multiple dispatchers

Multi Unique

ConfiguredO(n) Optimal algorithm

NP complete: Greedy 2-approx. and PTAS algs

Unconfigured NP complete:Greedy 2-approx.

NP complete: work in progress

Approaches

Multi Unique

ConfiguredO(n) Optimal algorithm

NP complete: Greedy 2-approx. and PTAS algs

Unconfigured NP complete:Greedy 2-approx.

NP complete: work in progress

Optimization objective: min(max sj/Sj or dj/Dj)