Whole-Page Optimization and Submodular Welfare Maximization with Online Bidders

In the context of online ad serving, display ads may appear on different types of webpages, where each page includes several ad slots and therefore multiple ads can be shown on each page. The set of ads that can be assigned to ad slots of the same page needs to satisfy various prespecified constraints including exclusion constraints, diversity constraints, and the like. Upon arrival of a user, the ad serving system needs to allocate a set of ads to the current webpage respecting these per-page allocation constraints. Previous slot-based settings ignore the important concept of a page and may lead to highly suboptimal results in general. In this article, motivated by these applications in display advertising and inspired by the submodular welfare maximization problem with online bidders, we study a general class of page-based ad allocation problems, present the first (tight) constant-factor approximation algorithms for these problems, and confirm the performance of our algorithms experimentally on real-world datasets. A key technical ingredient of our results is a novel primal-dual analysis for handling free disposal, which updates dual variables using a “level function” instead of a single level and unifies with previous analyses of related problems. This new analysis method allows us to handle arbitrarily complicated allocation constraints for each page. Our main result is an algorithm that achieves a 1 &minus frac 1 e &minus o(1)-competitive ratio. Moreover, our experiments on real-world datasets show significant improvements of our page-based algorithms compared to the slot-based algorithms. Finally, we observe that our problem is closely related to the submodular welfare maximization (SWM) problem. In particular, we introduce a variant of the SWM problem with online bidders and show how to solve this problem using our algorithm for whole-page optimization.postprin

Designing cost-sharing methods for Bayesian games

We study the design of cost-sharing protocols for two fundamental resource allocation problems, the Set Cover and the Steiner Tree Problem, under environments of incomplete information (Bayesian model). Our objective is to design protocols where the worst-case Bayesian Nash equilibria, have low cost, i.e. the Bayesian Price of Anarchy (PoA) is minimized. Although budget balance is a very natural requirement, it puts considerable restrictions on the design space, resulting in high PoA. We propose an alternative, relaxed requirement called budget balance in the equilibrium (BBiE).We show an interesting connection between algorithms for Oblivious Stochastic optimization problems and cost-sharing design with low PoA. We exploit this connection for both problems and we enforce approximate solutions of the stochastic problem, as Bayesian Nash equilibria, with the same guarantees on the PoA. More interestingly, we show how to obtain the same bounds on the PoA, by using anonymous posted prices which are desirable because they are easy to implement and, as we show, induce dominant strategies for the players

Primal dual gives almost optimal energy efficient online algorithms

We consider the problem of online scheduling of jobs on unrelated machines with dynamic speed scaling to minimize the sum of energy and weighted flow time. We give an algorithm with an almost optimal competitive ratio for arbitrary power functions. (No earlier results handled arbitrary power functions for minimizing flow time plus energy with unrelated machines.) For power functions of the form f(s) = s^alpha for some constant alpha > 1, we get a competitive ratio of O(alpha/log(alpha)), improving upon a previous competitive ratio of O(alpha^2) by Anand et al., along with a matching lower bound of . Further, in the resource augmentation model, with a 1+epsilon speed up, we give a O(1/epsilon) competitive algorithm, with essentially the same techniques, improving the bound of O(1/epsilon^2) by Gupta et al. and matching the bound of Anand et al. [3] for the special case of fixed speed unrelated machines. Unlike the previous results most of which used an amortized local competitiveness argument or dual fitting methods, we use a primal-dual method, which is useful not only to analyze the algorithms but also to design the algorithm itself. Copyright © 2014 by the Society for Industrial and Applied Mathematics.link_to_OA_fulltex

Speed scaling in the non-clairvoyant model

In recent years, there has been a growing interest in speed scaling algorithms, where a set of jobs need to be scheduled on a machine with variable speed so as to optimize the flow-times of the jobs and the energy consumed by the machine. A series of results have culminated in constant-competitive algorithms for this problem in the clairvoyant model, i.e., when job parameters are revealed on releasing a job (Bansal, Pruhs, and Stein, SODA 2007; Bansal, Chan, and Pruhs, SODA 2009). Our main contribution in this paper is the first constant-competitive speed scaling algorithm in the nonclairvoyant model, which is typically used in the scheduling literature to model practical settings where job volume is revealed only after the job has been completely processed. Unlike in the clairvoyant model, the speed scaling problem in the non-clairvoyant model is non-trivial even for a single job. Our non-clairvoyant algorithm is defined by using the existing clairvoyant algorithm in a novel inductive way, which then leads to an inductive analytical tool that may be of independent interest for other online optimization problems. We also give additional algorithmic results and lower bounds for speed scaling on multiple identical parallel machines.link_to_OA_fulltex

I.R.C. § 152(b)(5) and Victorian Morality in Contemporary Life

State and local governments, for the most part, no longer attempt to use the criminal law to impose a uniform standard of personal morals concerning intimate behavior. Some states have repealed outright the laws originally enacted to give legal sanction to religion-based standards of sexual conduct. In a substantial number of other states, statute books still include criminal laws prohibiting adultery, cohabitation, fornication, and sodomy; however, prosecutions for private, adult consensual acts violating those prohibitions are essentially nonexistent. By adopting antidiscrimination laws that establish rights to equal treatment without regard to private living arrangements, many states have in fact taken positive actions that cast doubt on the continued validity of aged morals statutes. Though not without atavism the courts have not opposed, and have sometimes advanced, the movement away from government involvement in intimate affairs. Nearly ten years ago a New York Supreme Court justice described a retirement-age couple\u27s living together without formal marriage as an enlightened and realistic approach to modern day living ...

Whole-page optimization and submodular welfare maximization with online bidders

In the context of online ad serving, display ads may appear on different types of web-pages, where each page includes several ad slots and therefore multiple ads can be shown on each page. The set of ads that can be assigned to ad slots of the same page needs to satisfy various pre-specified constraints including exclusion constraints, diversity constraints, and the like. Upon arrival of a user, the ad serving system needs to allocate a set of ads to the current web-page respecting these per-page allocation constraints. Previous slot-based settings ignore the important concept of a page, and may lead to highly suboptimal results in general. In this paper, motivated by these applications in display advertising and inspired by the submodular welfare maximization problem with online bidders, we study a general class of page-based ad allocation problems, present the first (tight) constant-factor approximation algorithms for these problems, and confirm the performance of our algorithms experimentally on real-world data sets. A key technical ingredient of our results is a novel primal-dual analysis for handling free-disposal, which updates dual variables using a \level function" instead of a single level, and unifies with previous analy- ses of related problems. This new analysis method allows us to handle arbitrarily complicated allocation constraints for each page. Our main result is an algorithm that achieves a 1 1 e o(1) competitive ratio. Moreover, our experiments on real-world data sets show significant improvements of our page-based algorithms compared to the slot-based algorithms. Finally, we observe that our problem is closely related to the submodular welfare maximization (SWM) problem. In particular, we introduce a variant of the SWM problem with online bidders, and show how to solve this problem using our algorithm for whole page optimization. Copyright © 2013 ACM.link_to_subscribed_fulltex