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Published byRickey Roxbury Modified over 2 years ago

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

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Big vs. Small

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

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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

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Previous Work

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The Main Result

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Approaches for ONMCF with high demands

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Approaches for ONMCF with high, demands, cont.

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An (simple) Example

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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

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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

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Extending the Framework Formally,

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The Tri-Criteria Oracle

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The Main Result

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Mixed Demands

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Further Extensions

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