Reorganization in Network Regions for Optimality and Fairness

1. Reorganization in Network Regions for Optimality and Fairness Robert E. Beverly IV, MSc Thesis

2. Motivation • Drawbacks of flooding: • Nodes receive messages more than once • Nodes receive messages they cannot service • Free-riding

3. Solution • Network reorganization Nodes can select their neighbors • Messages reach nodes that can service them • Flooding horizon reduced => less duplicates • Free-riders are ostracized • Super-peers can solve first two problems

4. Previous Work • Super-peers scheme relies on the altruism of the super-peers • Semantic-Overlay-Networks • Interest-based shortcuts • Gia

5. Interest-based similarity • A node searching for items of type A while holding items of type B, will have trouble connecting with nodes holding items of type B, if they search for items of type B • In 60% of nodes A=B

6. Design: Definitions • Ideal network: Complete graph • Fair network: Each node’s query hit rate is proportional to the query hits it provides to its neighbors • Utility optimal network: selfishness vs. altruism

7. Design: Idea • Each node tries to connect to nodes that increase its utility (provide the content it needs) and disconnect from nodes that decrease it (relay traffic to it without providing the desired content. • Organization is dynamic and not rigid. Reorganization process is independent for each node.

8. Design: Utility • Node utility: sqrt(M) – a*L • M = query hit rate • L = incoming queries rate • a = 10

9. Implementation with SuperPeers • Leaves periodically connect to a new SuperPeer. • Leaves periodically compute their utility function for each SuperPeer and drop connections to SuperPeers with utility < 0 • Utility raises but is bounded by the max # of leaves per SuperPeer.

10. Flat Implementation: Modifications • A neighbor that relays heavy traffic must not be immediately dropped. In contrast to SuperPeers, nodes can choose their neighbors. • Utility per subs et of neighbors instead of per neighbor

11. Flat Implementation: Algorithm • Connect to a random new node. Initial satisRank = 15 • Compute utilities for every subset of neighbors. • Increase satisfaction rank for each neighbor in best neighbor subset • Drop neighbor x with prob = e-0.14*satisRank[x] • prob(satisRank[x] = 0) = 1 • prob(satisRank[x] = 15) = 0.12 • 50% increase after 5 steps (due to the -0.14 factor)

12. Analysis: The cost of being selfish • Anarchy (A node servicing many free-riders) • Indifference (A node whose benefit equals its cost) • Ordering: To identify a subset of two nodes as optimal, they must neighbors at the same time. Checking them sequentially will reject them (solved by decaying satisfaction mechanism)

13. Evaluation • SuperPeers scheme aggregate utility: 213 at TTL = 4, -289 at TTL=5 (because of duplicate queries?!) • Degrees of selfishness: • Risk-Adverse Altruistic Optimality • Equilibrium Optimality • As seen before, both models have lower max aggregate utilization. (200 and 40 resp.) • This max utilization incurs at highly disconnected graphs (65 and 95% resp.) because of the bartering problem

14. Redesign • The algorithm described previously matches the equilibrium optimality. • Epsilon-equilibrium: Decrease selfishness/ increase connectivity • From all neighbor subsets with utilities [max-epsilon, max] choose subset with largest size

15. Results • With epsilon = 0.1 => 60% of graph is connected

16. Results • Utilization 120 in approx. 8 hrs

17. Results • More (?) nodes have higher individual utilization than lower compared with the SuperPeers scheme