Motivated by the problem of packing Virtual Machines on physical servers in the cloud, we study the problem of online stochastic bin packing under two settings -- packing with permanent items, and packing under item departures. In the setting with permanent items, we present the first truly distribution-oblivious bin packing heuristic that achieves O(√n) regret compared to OPT for all distributions. Our algorithm is essentially gradient descent on suitably defined Lagrangian relaxation of the bin packing Linear Program. We also prove guarantees of our heuristic against non i.i.d. input using a randomly delayed Lyapunov function to smoothen the input.

We introduce a new notion of classification accuracy based on the top $\tau$-quantile values of a scoring function, a relevant criterion in a number of problems arising for search engines. We define an algorithm optimizing a convex surrogate of the corresponding loss, and show how its solution can be obtained by solving several convex optimization problems. We also present margin-based guarantees for this algorithm based on the $\tau$-quantile of the functions in the hypothesis set. Finally, we report the results of several experiments evaluating the performance of our algorithm. In a comparison in a bipartite setting with several algorithms seeking high precision at the top, our algorithm achieves a better performance in precision at the top.

Display advertising is the graphical advertising on the World Wide Web (WWW) that appears next to content on web pages, instant messaging (IM) applications, email, etc. Over the past decade, display ads have evolved from simple banner and pop-up ads to include various combinations of text, images, audio, video, and animations. As a market segment, display continues to show substantial growth potential, as evidenced by companies such as Microsoft, Yahoo, and Google actively vying for market share. As a sales process, display ads are typically sold in packages, the result of negotiations between sales and advertising agents. A key component to any successful business model in display advertising is sound pricing. Main objectives for on-line publishers (e.g. Amazon, YouTube, CNN) are maximizing revenue while managing their available inventory appropriately, and pricing must reflect these considerations.

We investigate a widely popular least-recently-used (LRU) cache replacement algorithm with semiMarkov modulated requests. SemiMarkov processes provide the flexibility for modeling strong statistical correlation, including the broadly reported long-range dependence in the World Wide Web page request patterns. When the frequency of requesting a page n is equal to the generalized Zipf's law c/n/sup /spl alpha//, /spl alpha/ > 1, our main result shows that the cache fault probability is asymptotically, for large cache sizes, the same as in the corresponding LRU system with i.i.d. requests. This appears to be the first explicit average case analysis of LRU caching with statistically dependent request sequences. The surprising insensitivity of LRU caching performance demonstrates its robustness to changes in document popularity. Furthermore, we show that the derived asymptotic result and simulation experiments are in excellent agreement, even for relatively small cache sizes. The potential of using our results in predicting the behavior of Web caches is tested using actual, strongly correlated, proxy server access traces.