Nicole Immorlica

Semantic similarity between search engine queries using temporal correlation

We investigate the idea of finding semantically related search engine queries based on their temporal correlation; in other words, we infer that two queries are related if their popularities behave similarly over time. To this end, we first define a new measure of the temporal correlation of two queries based on the correlation coefficient of their frequency functions. We then conduct extensive experiments using our measure on two massive query streams from the MSN search engine, revealing that this technique can discover a wide range of semantically similar queries. Finally, we develop a method of efficiently finding the highest correlated queries for a given input query using far less space and time than the naive approach, making real-time implementation possible.

Multi-unit auctions with budget-constrained bidders

We study a multi-unit auction with multiple bidders, each of whom has a private valuation and a budget. The truthful mechanisms of such an auction are characterized, in the sense that, under standard assumptions, we prove that it is impossible to design a non-trivial truthful auction which allocates all units, while we provide the design of an asymptotically revenue-maximizing truthful mechanism which may allocate only some of the units. Our asymptotic parameter is a budget dominance parameter which measures the size of the budget of a single agent relative to the maximum revenue. We discuss the relevance of these results for the design of Internet ad auctions.

A Knapsack Secretary Problem with Applications

We consider situations in which a decision-maker with a fixed budget faces a sequence of options, each with a cost and a value, and must select a subset of them online so as to maximize the total value. Such situations arise in many contexts, e.g., hiring workers, scheduling jobs, and bidding in sponsored search auctions. This problem, often called the online knapsack problem, is known to be inapproximable. Therefore, we make the enabling assumption that elements arrive in a randomorder. Hence our problem can be thought of as a weighted version of the classical secretary problem, which we call the knapsack secretary problem. Using the random-order assumption, we design a constant-competitive algorithm for arbitrary weights and values, as well as a e-competitive algorithm for the special case when all weights are equal (i.e., the multiple-choice secretary problem). In contrast to previous work on online knapsack problems, we do not assume any knowledge regarding the distribution of weights and values beyond the fact that the order is random.

Power optimization in fault-tolerant topology control algorithms for wireless multi-hop networks

In ad hoc wireless networks, it is crucial to minimize power consumption while maintaining key network properties. This work studies power assignments of wireless devices that minimize power while maintaining k-fault tolerance. Specifically, we require all links established by this power setting be symmetric and form a k-vertex connected subgraph of the network graph. This problem is known to be NP-hard. We show current heuristic approaches can use arbitrarily more power than the optimal solution. Hence, we seek approximation algorithms for this problem. We present three approximation algorithms. The first algorithm gives an O(kalpha)-approximation where is the best approximation factor for the related problem in wired networks (the best alpha so far is O(log k)). With a more careful analysis, we show our second (slightly more complicated) algorithm is an O(k)-approximation. Our third algorithm assumes that the edge lengths of the network graph form a metric. In this case, we present simple and practical distributed algorithms for the cases of 2- and 3-connectivity with constant approximation factors. We generalize this algorithm to obtain an O(k2c+2)-approximation for general k-connectivity (2 les c les 4 is the power attenuation exponent). Finally, we show that these approximation algorithms compare favorably with existing heuristics. We note that all algorithms presented in this paper can be used to minimize power while maintaining -edge connectivity with guaranteed approximation factors. Recently, different set of authors used the notion of k-connectivity and the results of this paper to deal with the fault-tolerance issues for static wireless network settings.

A first look at peer-to-peer worms: threats and defenses

Peer-to-peer (P2P) worms exploit common vulnerabilities in member hosts of a P2P network and spread topologically in the P2P network, a potentially more effective strategy than random scanning for locating victims. This paper describes the danger posed by P2P worms and initiates the study of possible mitigation mechanisms. In particular, the paper explores the feasibility of a self-defense infrastructure inside a P2P network, outlines the challenges, evaluates how well this defense mechanism contains P2P worms, and reveals correlations between containment and the overlay topology of a P2P network. Our experiments suggest a number of design directions to improve the resilience of P2P networks to worm attacks.

Correlation Clustering with Partial Information

We consider the following general correlation-clustering problem [1]: given a graph with real edge weights (both positive and negative), partition the vertices into clusters to minimize the total absolute weight of cut positive edges and uncut negative edges. Thus, large positive weights (representing strong correlations between endpoints) encourage those endpoints to belong to a common cluster; large negative weights encourage the endpoints to belong to different clusters; and weights with small absolute value represent little information. In contrast to most clustering problems, correlation clustering specifies neither the desired number of clusters nor a distance threshold for clustering; both of these parameters are effectively chosen to be the best possible by the problem definition.

Online auctions and generalized secretary problems

We present generalized secretary problems as a framework for online auctions. Elements, such as potential employees or customers, arrive one by one online. After observing the value derived from an element, but without knowing the values of future elements, the algorithm has to make an irrevocable decision whether to retain the element as part of a solution, or reject it. The way in which the secretary framework differs from traditional online algorithms is that the elements arrive in uniformly random order. Many natural online auction scenarios can be cast as generalized secretary problems, by imposing natural restrictions on the feasible sets. For many such settings, we present surprisingly strong constant factor guarantees on the expected value of solutions obtained by online algorithms. The framework is also easily augmented to take into account time-discounted revenue and incentive compatibility. We give an overview of recent results and future research directions.

Click fraud resistant methods for learning click-through rates

In pay-per-click online advertising systems like Google, Overture, or MSN, advertisers are charged for their ads only when a user clicks on the ad. While these systems have many advantages over other methods of selling online ads, they suffer from one major drawback. They are highly susceptible to a particular style of fraudulent attack called click fraud. Click fraud happens when an advertiser or service provider generates clicks on an ad with the sole intent of increasing the payment of the advertiser. Leaders in the pay-per-click marketplace have identified click fraud as the most significant threat to their business model. We demonstrate that a particular class of learning algorithms, called click-based algorithms, are resistant to click fraud in some sense. We focus on a simple situation in which there is just one ad slot, and show that fraudulent clicks can not increase the expected payment per impression by more than o(1) in a click-based algorithm. Conversely, we show that other common learning algorithms are vulnerable to fraudulent attacks.

A Simple and Approximately Optimal Mechanism for an Additive Buyer

We consider a monopolist seller with n heterogeneousitems, facing a single buyer. The buyer hasa value for each item drawn independently according to(non-identical) distributions, and his value for a set ofitems is additive. The seller aims to maximize his revenue.It is known that an optimal mechanism in this setting maybe quite complex, requiring randomization [19] and menusof infinite size [15]. Hart and Nisan [17] have initiated astudy of two very simple pricing schemes for this setting:item pricing, in which each item is priced at its monopolyreserve; and bundle pricing, in which the entire set ofitems is priced and sold as one bundle. Hart and Nisan [17]have shown that neither scheme can guarantee more thana vanishingly small fraction of the optimal revenue. Insharp contrast, we show that for any distributions, thebetter of item and bundle pricing is a constant-factorapproximation to the optimal revenue. We further discussextensions to multiple buyers and to valuations that arecorrelated across items.

First-price path auctions

We study first-price auction mechanisms for auctioning flow between given nodes in a graph. A first-price auction is any auction in which links on winning paths are paid their bid amount; the designer has flexibility in specifying remaining details. We assume edges are independent agents with fixed capacities and costs, and their objective is to maximize their profit. We characterize all strong ε-Nash equilibria of a first-price auction, and show that the total payment is never significantly more than, and often less than, the well known dominant strategy Vickrey-Clark-Groves mechanism. We then present a randomized version of the first-price auction for which the equilibrium condition can be relaxed to ε-Nash equilibrium. We next consider a model in which the amount of demand is uncertain, but its probability distribution is known. For this model, we show that a simple ex ante first-price auction may not have any ε-Nash equilibria. We then present a modified mechanism with 2-parameter bids which does have an ε-Nash equilibrium. For a randomized version of this 2-parameter mechanism we characterize the set of all eNEs and prove a bound on the total payment in any eNE.