1. Online Multi-Commodity Flow with High Demands Guy Even EE School, Tel-Aviv University Moti Medina EE School, Tel-Aviv University

2. Big vs. Small

3. ONMCF OMCF Problem Definition ONMCF: Online Multi-Commodity Flow with High Demands

4. We consider an online maximization problem: – Competitive analysis. For every input sequence σ, | Alg(σ)| 1/ρ |OPT(σ)|. – Alg – deterministic online algorithm. – OPT – offline optimum. – | Alg | - total benefit of algorithm Alg. – ρ – competitive ratio Competitive Analysis

5. Previous Work

6. The Main Result

7. Approaches for ONMCF with high demands

8. Approaches for ONMCF with high, demands, cont.

9. An (simple) Example

10. Techniques Main Technique – Extension of [AAP93] and [BN06] Integrally packing paths by a centralized online algorithm. log n – competitive. Edge costs: exponential in the load of the edge. Oracle: Finds a shortest path. Alg : – If the cost of the path is higher then its benefit, then reject, – Otherwise, accept. Resource ManagerOracle

11. Techniques Main Technique – The Reduction Now, the requests are flow requests. Every request increases the load of edges that it uses. – The edge cost is updated. The Oracle finds a min-cost flow that fully serves the request. The Oracle – Is an offline tri-criteria oracle. » Approximated, augmenting, granular. Resource ManagerOracle

12. Extending the Framework Formally,

13. The Tri-Criteria Oracle

14. The Main Result

15. Mixed Demands

16. Further Extensions