Online Stochastic Matching Barna Saha Vahid Liaghat.

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Presentation transcript:

Online Stochastic Matching Barna Saha Vahid Liaghat

Matching? Adwords Bidders

Matching? Adword Types Bidders

Offline LP Relaxation

Online Matching Adversarial, Unknown Graph Vazirani et al.[1] 1-1/e can’t do better Random Arrival, Unknown Graph Goel & Mehta[2] 1-1/e can’t do better than 0.83 i.i.d Model: Known Graph and Arrival Ratios – Integral: Bahmani et al.[3] Can’t do better than Saberi et al.[4] – General: Saberi et al.[4] Can’t do better than 0.823

i.i.d. Model

Fractional Matching

Non-Adaptive Algorithm

Algorithm 1 - Analysis

Adaptive Algorithm - idea

Adaptive Algorithm - partitions

Adaptive Algorithm

Upper Bounds

Questions?

References [1] R. M. Karp, U. V. Vazirani, and V. V. Vazirani. An optimal algorithm for online bipartite matching. In STOC, pages 352–358. ACM, [2] G. Goel and A. Mehta. Online budgeted matching in random input models with applications to adwords. In SODA, pages 982–991, [3] B. Bahmani and M. Kapralov. Improved bounds for online stochastic matching. In ESA, pages 170–181, [4] V. H. Manshadi, S. Oveis Gharan, A. Saberi. Online Stochastic Matching: Online Actions Based on Offline Statistics. In SODA, 2011.

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