Gagan Aggarwal

Truthful auctions for pricing search keywords

We present a truthful auction for pricing advertising slots on a web-page assuming that advertisements for different merchants must be ranked in decreasing order of their (weighted) bids. This captures both the Overture model where bidders are ranked in order of the submitted bids, and the Google model where bidders are ranked in order of the expected revenue (or utility) that their advertisement generates. Assuming separable click-through rates, we prove revenue-equivalence between our auction and the non-truthful next-price auctions currently in use.

Anonymizing tables

We consider the problem of releasing tables from a relational database containing personal records, while ensuring individual privacy and maintaining data integrity to the extent possible. One of the techniques proposed in the literature is k-anonymization. A release is considered k-anonymous if the information for each person contained in the release cannot be distinguished from at least k–1 other persons whose information also appears in the release. In the k-Anonymityproblem the objective is to minimally suppress cells in the table so as to ensure that the released version is k-anonymous. We show that the k-Anonymity problem is NP-hard even when the attribute values are ternary. On the positive side, we provide an O(k)-approximation algorithm for the problem. This improves upon the previous best-known O(klog k)-approximation. We also give improved positive results for the interesting cases with specific values of k — in particular, we give a 1.5-approximation algorithm for the special case of 2-Anonymity, and a 2-approximation algorithm for 3-Anonymity.

Complexities for Generalized Models of Self-Assembly

In this paper, we extend Rothemund and Winfrees examination of the tile complexity of tile self-assembly [6]. They provided a lower bound of Ω(log <i>N</i>/log log <i>N</i>) on the tile complexity of assembling an <i>N</i> × <i>N</i> square for almost all <i>N</i>. Adleman et al. [1] gave a construction which achieves this bound. We consider whether the tile complexity for self-assembly can be reduced through several natural generalizations of the model. One of our results is a tile set of size <i>O</i>(√log <i>N</i>) which assembles an <i>N</i> × <i>N</i> square in a model which allows flexible glue strength between non-equal glues (This was independently discovered in [3]). This result is matched by a lower bound dictated by Kolmogorov complexity. For three other generalizations, we show that the Ω(log <i>N</i>/log log <i>N</i>) lower bound applies to <i>N</i> × <i>N</i> squares. At the same time, we demonstrate that there are some other shapes for which these generalizations allow reduced tile sets. Specifically, for thin rectangles with length <i>N</i> and width <i>k</i>, we provide a tighter lower bound of Ω(<i>N</i>(1/<i>k</i>)/<i>k</i>) for the standard model, yet we also give a construction which achieves <i>O</i>(log <i>N</i>/log log <i>N</i>) complexity in a model in which the temperature of the tile system is adjusted during assembly. We also investigate the problem of verifying whether a given tile system uniquely assembles into a given shape, and show that this problem is NP-hard.

Secure Computation of the kth-Ranked Element

Given two or more parties possessing large, confidential datasets, we consider the problem of securely computing the k th -ranked element of the union of the datasets, e.g. the median of the values in the datasets. We investigate protocols with sublinear computation and communication costs. In the two-party case, we show that the k th -ranked element can be computed in log k rounds, where the computation and communication costs of each round are O(log M), where log M is the number of bits needed to describe each element of the input data. The protocol can be made secure against a malicious adversary, and can hide the sizes of the original datasets. In the multi-party setting, we show that the k th -ranked element can be computed in log M rounds, with O(s log M) overhead per round, where s is the number of parties. The multi-party protocol can be used in the two-party case and can also be made secure against a malicious adversary.

General auction mechanism for search advertising

In sponsored search, a number of advertising slots is available on a search results page, and have to be allocated among a set of advertisers competing to display an ad on the page. This gives rise to a bipartite matching market that is typically cleared by the way of an automated auction. Several auction mechanisms have been proposed, with variants of the Generalized Second Price (GSP) being widely used in practice. There is a rich body of work on bipartite matching markets that builds upon the stable marriage model of Gale and Shapley and the assignment model of Shapley and Shubik. This line of research offers deep insights into the structure of stable outcomes in such markets and their incentive properties. In this paper, we model advertising auctions in terms of an assignment model with linear utilities, extended with bidder and item specific maximum and minimum prices. Auction mechanisms like the commonly used GSP or the well-known Vickrey-Clarke-Groves (VCG) can be interpreted as simply computing a bidder-optimal stable matching in this model, for a suitably defined set of bidder preferences, but our model includes much richer bidders and preferences. We prove that in our model the existence of a stable matching is guaranteed, and under a non-degeneracy assumption a bidder-optimal stable matching exists as well. We give an algorithm to find such matching in polynomial time, and use it to design truthful mechanism that generalizes GSP, is truthful for profit-maximizing bidders, correctly implements features like bidder-specific minimum prices and position-specific bids, and works for rich mixtures of bidders and preferences. Our main technical contributions are the existence of bidder-optimal matchings and strategyproofness of the resulting mechanism, and are proved by induction on the progress of the matching algorithm.

Algorithms for Multi-product Pricing

In the information age, the availability of data on consumer profiles has opened new possibilities for companies to increase their revenue via data mining techniques. One approach has been to strategically set prices of various products, taking into account the profiles of consumers. We study algorithms for the multi-product pricing problem, where, given consumer preferences among products, their budgets, and the costs of production, the goal is to set prices of multiple products from a single company, so as to maximize the overall revenue of the company. We present approximation algorithms as well as negative results for several variants of the multi-product pricing problem, modeling different purchasing patterns and market assumptions.

Vision paper: enabling privacy for the paranoids

P3P [23, 24] is a set of standards that allow corporations to declare their privacy policies. Hippocratic Databases [6] have been proposed to implement such policies within a corporations datastore. From an end-user individuals point of view, both of these rest on an uncomfortable philosophy of trusting corporations to protect his/her privacy. Recent history chronicles several episodes when such trust has been willingly or accidentally violated by corporations facing bankruptcy courts, civil subpoenas or lucrative mergers. We contend that data management solutions for information privacy must restore controls in the individuals hands. We suggest that enabling such control will require a radical re-think on modeling, release, and management of personal data.

Bidding to the top: VCG and equilibria of position-based auctions

Many popular search engines run an auction to determine the placement of advertisements next to search results. Current auctions at Google and Yahoo! let advertisers specify a single amount as their bid in the auction. This bid is interpreted as the maximum amount the advertiser is willing to pay per click on its ad. When search queries arrive, the bids are used to rank the ads linearly on the search result page. Advertisers seek to be high on the list, as this attracts more attention and more clicks. The advertisers pay for each user who clicks on their ad, and the amount charged depends on the bids of all the advertisers participating in the auction. We study the problem of ranking ads and associated pricing mechanisms when the advertisers not only specify a bid, but additionally express their preference for positions in the list of ads. In particular, we study prefix position auctions where advertiser i can specify that she is interested only in the top κi positions. We present a simple allocation and pricing mechanism that generalizes the desirable properties of current auctions that do not have position constraints. In addition, we show that our auction has an envy-free [1] or symmetric [2] Nash equilibrium with the same outcome in allocation and pricing as the well-known truthful Vickrey-Clarke-Groves (VCG) auction. Furthermore, we show that this equilibrium is the best such equilibrium for the advertisers in terms of the profit made by each advertiser. We also discuss other position-based auctions.

The load rebalancing problem

In the classical load balancing or multiprocessor scheduling problem, we are given a sequence of jobs of varying sizes and are asked to assign each job to one of the m empty processors. A typical objective is to minimize makespan, the load on the heaviest loaded processor. Since in most real world scenarios the load is a dynamic measure, the initial assignment may be not remain optimal with time. Motivated by such considerations in a variety of systems, we formulate the problem of load rebalancing --- given a possibly suboptimal assignment of jobs to processors, relocate a set of the jobs so as to decrease the makespan. Specifically, the goal is to achieve the best possible makespan under the constraint that no more than k jobs are relocated. We also consider a generalization of this problem where there is an arbitrary cost function associated with each job relocation. Since the problem is clearly NP-hard, we focus on approximation algorithms. We construct a sophisticated algorithm which achieves a 1.5-approximation, with near linear running time. We also show that the problem has a PTAS, resolving the complexity issue. Finally, we investigate the approximability of several extensions of the rebalancing model.

Derandomization of auctions

We study the problem of designing seller-optimal auctions, i.e. auctions where the objective is to maximize revenue. Prior to this work, the only auctions known to be approximately optimal in the worst case employed randomization. Our main result is the existence of deterministic auctions that approximately match the performance guarantees of these randomized auctions. We give a fairly general derandomization technique for turning any randomized mechanism into an asymmetric deterministic one with approximately the same revenue. In doing so, we bypass the impossibility result for symmetric deterministic auctions and show that asymmetry is nearly as powerful as randomization for solving optimal mechanism design problems. Our general construction involves solving an exponential-sized flow problem and thus is not polynomial-time computable. To complete the picture, we give an explicit polynomial-time construction for derandomizing a specific auction with good worst-case revenue. Our results are based on toy problems that have a flavor similar to the hat problem from [3].