Abstract: An auction mechanism that decouples advertisement selection from advertisement ranking is described herein. A page to be displayed on a client computing device has a plurality of advertisement positions. Responsive to receipt of data that is indicative of content to be included on the page, a plurality of bids corresponding to a respective plurality of advertisements are received, wherein each bid has a respective bid value. Further, a respective quality score is computed for each advertisement responsive to the receipt of the data. A subset of advertisements are selected from the plurality of advertisements based upon their respective bid values. Subsequently, the selected advertisements are ranked and assigned to the advertisement positions based upon their quality scores, which are independent of their bid values.

Abstract: Various embodiments provide offline algorithms for resource allocation. A known set of “offline” requests may be matched to available resources using an online resource allocation algorithm that models the offline resource allocation problem as though the requests were received stochastically. Requests may be scaled and then sampled to provide random, stochastic input for the online resource allocation algorithm. For each request, resources are allocated to the request by evaluating multiple options based upon shadow costs assigned to resources associated with the different options. After each request is processed, an adjustment is made to the shadow costs for remaining resources to reflect differences in rates for allocation and/or consumption of the resources and the updated shadow costs are used for a subsequent request. A scaled resource allocation determined using sampled requests in this manner may be scaled back up to obtain a solution for the offline resource allocation problem.

Abstract: Various embodiments provide offline algorithms for resource allocation. A known set of “offline” requests may be matched to available resources using an online resource allocation algorithm that models the offline resource allocation problem as though the requests were received stochastically. Requests may be scaled and then sampled to provide random, stochastic input for the online resource allocation algorithm. For each request, resources are allocated to the request by evaluating multiple options based upon shadow costs assigned to resources associated with the different options. After each request is processed, an adjustment is made to the shadow costs for remaining resources to reflect differences in rates for allocation and/or consumption of the resources and the updated shadow costs are used for a subsequent request. A scaled resource allocation determined using sampled requests in this manner may be scaled back up to obtain a solution for the offline resource allocation problem.

Abstract: Various embodiments provide online algorithms for resource allocation. In one or more embodiments, requests for resources from a service provider are received stochastically. For each request, different options for satisfying the request are evaluated based in part upon shadow costs (e.g., unit costs) that are assigned to resources associated with the different options. One of the options may be selected by optimizing an objective function that accounts for the shadow costs. Resources for the selected option are allocated to the request and an adjustment is made to the shadow costs for remaining resources to reflect differences in rates for allocation and/or consumption of the resources. Thereafter, resources may be allocated to a subsequent request using the updated shadow costs and the costs are adjusted again. By updating shadow costs iteratively in this manner, an increasingly more accurate analysis of the objective function is achieved.