1. Analysis and algorithms of the construction of the minimum cost content-based publish/subscribe overlay Yaxiong Zhao and Jie Wu yaxiong.zhao@temple.edu Yaxiong Zhao will be graduating next summer!

2. Outline Introduction Analysis – Integer programming formulation – Two-stage approximation – Sub-channeling and multicast-based approximation Simulation results Q&A

3. Content-based pub/sub overlay Overlay networks built with the content- based pub/sub principals – Brokers, publishers and subscribers are connected with overlay links – Brokers are dedicated servers Do not publish or subscribe – Publishers and subscribers are called users collectively A user can publish and subscribe simultaneously

4. Problem formulation Given a set of brokers B, a large number of users U and a 1-dimensional content space C Constraints – Message generating function defined on C A density function Give the message rate of a publisher by integration – Users are not allowed to connect with each other Privacy – Each user must connect with one and only one broker Reduce cost and end-user complexity

5. Cont’d Objectives – Wire brokers and users into a connected overlay – Distribute traffic on overlay links – Achieve minimum cost for the bandwidth used

6. Outline Introduction Analysis – Integer programming formulation – Two-stage approximation – Sub-channeling and multicast-based approximation Simulation results Q&A

7. Complexity Reduce from the general Steiner tree problem – Steiner tree problem can be seen as a special case of the above problem with the following settings Identical fixed link costs One publisher All subscribers have an identical demand The general Steiner tree problem is NP-hard – Means that our problem unlikely has a efficient optimal solution

8. Integer programming formulation Two parts of the optimization – Access: the traffic between brokers and users C 1 – Core: the traffic between brokers C 2 The design of the approximation algorithms try to optimize these two parts – Separately or together x ij =1 if user i connects to broker j b i (out) outgoing traffic of user I c ij is the cost of the link between i and j c’ ij =1 the cost of the link between broker i and j F ij flow between broker i and j

9. Outline Introduction Analysis and solutions – Integer programming formulation – Two-stage approximation – Sub-channeling and multicast-based approximation Simulation results Q&A

10. Two-stage greedy packing Each user connects to the broker with which it has the lowest-cost overlay link – Minimize the peripheral cost Then connect all of the brokers using weighted shortest path – With routing cost as the link cost

11. A sample network and the results

12. Two-stage clustering Clustering publisher and subscriber pairs that have the lowest cost-to- bandwidth ratio Starting with biggest flow with decreasing order – Find the minimum cost path connecting the broker and the subscriber – Fix the links – Assign remaining flows

13. Outline Introduction Analysis and solutions – Integer programming formulation – Two-stage approximation – Sub-channeling and multicast-based approximation Simulation results Q&A

14. Sub-channeling and multicast We try to formulate the problem using multicast – This is achieved through sub-channeling – Use small sub-channel to approximate the event traffic on the entire content space

15. Cont’d Approximate the minimum-cost multicast through on each sub-channel – Using Minimum-spanning tree Obtain a network wiring for brokers and users on each sub-channel – For each user, the traffic volume passing from it to its chosen broker is recorded Choose a connection for each user according to the weighted probability obtained from the traffic volume – For each sub-channel the traffic volume/ for link L i is V i – The probability to choose this link is V i /∑V i

16. Outline Introduction Analysis – Integer programming formulation – Two-stage approximation – Sub-channeling and multicast-based approximation Simulation results Q&A

17. Simulation settings 1000 to 10000 of users 100 to 1000 brokers – Keep a 10/1 ratio – A realistic setting in a cloud-computing era 100 networks of a given size – Obtain the average value Cost reduction ratio (CRR) – The cost achieved by random connection CR – The cost achieved by our algorithms CA – CRR = CR/CA

18. CRR vs. scale

19. CRR vs. Access-to-core link cost ratio

20. Q & A Send an Email to yaxiong.zhao@temple.edu if your questions are not answered