Yaxiong Zhao and Jie Wu yaxiong.zhao@temple.edu Yaxiong Zhao will be graduating next summer!

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principals • Brokers, publishers and subscribers are connected with overlay links • Brokers are dedicated servers • Do not publish or subscribe • Publishers and subscribers are called users collectively • A user can publish and subscribe simultaneously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 xij=1 if user i connects to broker j bi(out) outgoing traffic of user I cij is the cost of the link between i and j • Two parts of the optimization • Access: the traffic between brokers and users C1 • Core: the traffic between brokers C2 • The design of the approximation algorithms try to optimize these two parts • Separately or together c’ij=1 the cost of the link between broker i and j Fij 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 tothe weighted probability obtained from the traffic volume • For each sub-channel the traffic volume/ for link Li is Vi • The probability to choose this link is Vi/∑Vi

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