On the relation between complexity and uncertainty
Annals of Operations Research
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Contextual advertising by combining relevance with click feedback
Proceedings of the 17th international conference on World Wide Web
A contextual-bandit approach to personalized news article recommendation
Proceedings of the 19th international conference on World wide web
Collective attention and the dynamics of group deals
Proceedings of the 21st international conference companion on World Wide Web
Daily-deal selection for revenue maximization
Proceedings of the 21st ACM international conference on Information and knowledge management
Real-time bid optimization for group-buying ads
Proceedings of the 21st ACM international conference on Information and knowledge management
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Stochastic knapsack problems deal with selecting items with potentially random sizes and rewards so as to maximize the total reward while satisfying certain capacity constraints. A novel variant of this problem, where items are worthless unless collected in bundles, is introduced here. This setup is similar to the Groupon model, where a deal is off unless a minimum number of users sign up for it. Since the optimal algorithm to solve this problem is not practical, several adaptive greedy approaches with reasonable time and memory requirements are studied in detail - theoretically, as well as, experimentally. Worst case performance guarantees are provided for some of these greedy algorithms, while results of experimental evaluation demonstrate that they are much closer to optimal than what the theoretical bounds suggest. Applications include optimizing for online advertising pricing models where advertisers pay only when certain goals, in terms of clicks or conversions, are met. We perform extensive experiments for the situation where there are between two and five ads. For typical ad conversion rates, the greedy policy of selecting items having the highest individual expected reward obtains a value within 5% of optimal over 95% of the time for a wide selection of parameters.