Ioannis Giotis

Greedy bidding strategies for keyword auctions

How should players bid in keyword auctions such as those used by Google, Yahoo! and MSN?allWe consider greedy bidding strategies for a repeated auction on a single keyword, where in each round, each player chooses some optimal bid for the next round, assuming that the other players merely repeat their previous bid. We study the revenue, convergence and robustness properties of such strategies. Most interesting among these is a strategy we call the balanced bidding strategy (BB): it is known that BB has a unique fixed point with payments identical to those of the VCG mechanism. We show that if all players use the BB strategy and update each round, BB converges when the number of slots is at most 2, but does not always converge for 3 or more slots. On the other hand, we present a simple variant which is guaranteed to converge to the same fixed point for any number of slots. In a model in which only one randomly chosen player updates each round according to the BB strategy, we prove that convergence occurs with probability 1.We complement our theoretical results with empirical studies.

Correlation Clustering with a Fixed Number of Clusters.

We continue the investigation of problems concerning correlation clustering or clustering with qualitative information, which is a clustering formulation that has been studied recently [5, 7, 8, 3]. The basic setup here is that we are given as input a complete graph on n nodes (which correspond to nodes to be clustered) whose edges are labeled + (for similar pairs of items) and - (for dissimilar pairs of items). Thus we have only as input qualitative information on similarity and no quantitative distance measure between items. The quality of a clustering is measured in terms of its number of agreements, which is simply the number of edges it correctly classifies, that is the sum of number of - edges whose endpoints it places in different clusters plus the number of + edges both of whose endpoints it places within the same cluster.In this paper, we study the problem of finding clusterings that maximize the number of agreements, and the complementary minimization version where we seek clusterings that minimize the number of disagreements. We focus on the situation when the number of clusters is stipulated to be a small constant k. Our main result is that for every k, there is a polynomial time approximation scheme for both maximizing agreements and minimizing disagreements. (The problems are NP-hard for every k ≥ 2.) The main technical work is for the minimization version, as the PTAS for maximizing agreements follows along the lines of the property tester for Max k-CUT from [13].In contrast, when the number of clusters is not specified, the problem of minimizing disagreements was shown to be APX-hard [7], even though the maximization version admits a PTAS.

Correlation clustering with a fixed number of clusters

We continue the investigation of problems concerning correlation clustering or clustering with qualitative information, which is a clustering formulation that has been studied recently [5, 7, 8, 3]. The basic setup here is that we are given as input a complete graph on n nodes (which correspond to nodes to be clustered) whose edges are labeled + (for similar pairs of items) and - (for dissimilar pairs of items). Thus we have only as input qualitative information on similarity and no quantitative distance measure between items. The quality of a clustering is measured in terms of its number of agreements, which is simply the number of edges it correctly classifies, that is the sum of number of - edges whose endpoints it places in different clusters plus the number of + edges both of whose endpoints it places within the same cluster.In this paper, we study the problem of finding clusterings that maximize the number of agreements, and the complementary minimization version where we seek clusterings that minimize the number of disagreements. We focus on the situation when the number of clusters is stipulated to be a small constant k. Our main result is that for every k, there is a polynomial time approximation scheme for both maximizing agreements and minimizing disagreements. (The problems are NP-hard for every k ≥ 2.) The main technical work is for the minimization version, as the PTAS for maximizing agreements follows along the lines of the property tester for Max k-CUT from [13].In contrast, when the number of clusters is not specified, the problem of minimizing disagreements was shown to be APX-hard [7], even though the maximization version admits a PTAS.

Convergence of Position Auctions under Myopic Best-Response Dynamics

We study the dynamics of multiround position auctions, considering both the case of exogenous click-through rates and the case in which click-through rates are determined by an endogenous consumer search process. In both contexts, we demonstrate that dynamic position auctions converge to their associated static, envy-free equilibria. Furthermore, convergence is efficient, and the entry of low-quality advertisers does not slow convergence. Because our approach predominantly relies on assumptions common in the sponsored search literature, our results suggest that dynamic position auctions converge more generally.

An Alternate Proof of the Algorithmic Lovász Local Lemma

The algorithm for Lovasz Local Lemma by Moser and Tardos gives a constructive way to prove the existence of combinatorial objects satisfying a system of constraints. We present an alternative probabilistic analysis of the algorithm that does not involve reconstructing the history of the algorithm. We apply our technique to improve the best known upper bound to acyclic chromatic index.

On the Stability of Generalized Second Price Auctions with Budgets

The Generalized Second Price (GSP) auction used typically to model sponsored search auctions does not include the notion of budget constraints, which is present in practice. Motivated by this, we introduce the different variants of GSP auctions that take budgets into account in natural ways. We examine their stability by focusing on the existence of Nash equilibria and envy-free assignments. We highlight the differences between these mechanisms and find that only some of them exhibit both notions of stability. This shows the importance of carefully picking the right mechanism to ensure stable outcomes in the presence of budgets.

Cost-Sharing Models in Participatory Sensing

In Smart City and Participatory Sensing initiatives the key concept is for user communities to contribute sensor information and form a body of knowledge that can be exploited by innovative applications and data analytics services. A key aspect in all such platforms is that sensor information is not free but comes at a cost. As a result, these platforms may suffer due to insufficient sensor information made publicly available if applications do not share efficiently the cost of the sensor information they consume.