Georgios Amanatidis

Provably-secure schemes for basic query support in outsourced databases

In this paper, we take a closer look at the security of out-sourced databases (aka Database-as-the-Service or DAS), a topic of emerging importance. DAS allows users to store sensitive data on a remote, untrusted server and retrieve desired parts of it on request. At first we focus on basic, exact-match query functionality, and then extend our treatment to prefix-matching and, to a more limited extent, range queries as well. We propose several searchable encryption schemes that are not only practical enough for use in DAS in terms of query-processing efficiency but also provably-provide privacy and authenticity of data under new definitions of security that we introduce. The schemes are easy to implement and are based on standard cryptographic primitives such as block ciphers, symmetric encryption schemes, and message authentication codes. As we are some of the first to apply the provable-security framework of modern cryptography to this context, we believe our work will help to properly analyze future schemes and facilitate further research on the subject in general.

Approximation Algorithms for Computing Maximin Share Allocations

We study the problem of computing maximin share allocations, a recently introduced fairness notion. Given a set of n agents and a set of goods, the maximin share of an agent is the best she can guarantee to herself, if she is allowed to partition the goods in any way she prefers, into n bundles, and then receive her least desirable bundle. The objective then is to find a partition, where each agent is guaranteed her maximin share. Such allocations do not always exist, hence we resort to approximation algorithms. Our main result is a 2/3-approximation that runs in polynomial time for any number of agents and goods. This improves upon the algorithm of Procaccia and Wang (2014), which is also a 2/3-approximation but runs in polynomial time only for a constant number of agents. To achieve this, we redesign certain parts of the algorithm in Procaccia and Wang (2014), exploiting the construction of carefully selected matchings in a bipartite graph representation of the problem. Furthermore, motivated by the apparent difficulty in establishing lower bounds, we undertake a probabilistic analysis. We prove that in randomly generated instances, maximin share allocations exist with high probability. This can be seen as a justification of previously reported experimental evidence. Finally, we provide further positive results for two special cases arising from previous works. The first is the intriguing case of three agents, where we provide an improved 7/8-approximation. The second case is when all item values belong to {0, 1, 2}, where we obtain an exact algorithm.

Truthful Allocation Mechanisms Without Payments: Characterization and Implications on Fairness

We study the mechanism design problem of allocating a set of indivisible items without monetary transfers. Despite the vast literature on this very standard model, it still remains unclear how do truthful mechanisms look like. We focus on the case of two players with additive valuation functions and our purpose is twofold. First, our main result provides a complete characterization of truthful mechanisms that allocate all the items to the players. Our characterization reveals an interesting structure underlying all truthful mechanisms, showing that they can be decomposed into two components: a selection part where players pick their best subset among prespecified choices determined by the mechanism, and an exchange part where players are offered the chance to exchange certain subsets if it is favorable to do so. In the remaining paper, we apply our main result and derive several consequences on the design of mechanisms with fairness guarantees. We consider various notions of fairness, (indicatively, maximin share guarantees and envy-freeness up to one item) and provide tight bounds for their approximability. Our work settles some of the open problems in this agenda, and we conclude by discussing possible extensions to more players.

Coverage, Matching, and Beyond: New Results on Budgeted Mechanism Design

We study a type of reverse procurement auction problems in the presence of budget constraints. The general algorithmic problem is to purchase a set of resources, which come at a cost, so as not to exceed a given budget and at the same time maximize a given valuation function. This framework captures the budgeted version of several well known optimization problems, and when the resources are owned by strategic agents the goal is to design truthful and budget feasible mechanisms. We first obtain mechanisms with an improved approximation ratio for weighted coverage valuations, a special class of submodular functions. We then provide a general scheme for designing randomized and deterministic polynomial time mechanisms for a class of XOS problems. This class contains problems whose feasible set forms an independence system a more general structure than matroids, and some representative problems include, among others, finding maximum weighted matchings and maximum weighted matroid members. For most of these problems, only randomized mechanisms with very high approximation ratios were known prior to our results.

Comparing Approximate Relaxations of Envy-Freeness

In fair division problems with indivisible goods it is well known that one cannot have any guarantees for the classic fairness notions of envy-freeness and proportionality. As a result, several relaxations have been introduced, most of which in quite recent works. We focus on four such notions, namely envy-freeness up to one good (EF1), envy-freeness up to any good (EFX), maximin share fairness (MMS), and pairwise maximin share fairness (PMMS). Since obtaining these relaxations also turns out to be problematic in several scenarios, approximate versions of them have been considered. In this work, we investigate further the connections between the four notions mentioned above and their approximate versions. We establish several tight, or almost tight, results concerning the approximation quality that any of these notions guarantees for the others, providing an almost complete picture of this landscape. Some of our findings reveal interesting and surprising consequences regarding the power of these notions, e.g., PMMS and EFX provide the same worst-case guarantee for MMS, despite PMMS being a strictly stronger notion than EFX. We believe such implications provide further insight on the quality of approximately fair solutions.

An improved envy-free cake cutting protocol for four agents

We consider the classic cake-cutting problem of producing envy-free allocations, restricted to the case of four agents. The problem asks for a partition of the cake to four agents, so that every agent finds her piece at least as valuable as every other agents piece. The problem has had an interesting history so far. Although the case of three agents is solvable with less than 15 queries, for four agents no bounded procedure was known until the recent breakthroughs of Aziz and Mackenzie (STOC 2016, FOCS 2016). The main drawback of these new algorithms, however, is that they are quite complicated and with a very high query complexity. With four agents, the number of queries required is close to 600. In this work we provide an improved algorithm for four agents, which reduces the current complexity by a factor of 3.4. Our algorithm builds on the approach of Aziz and Mackenzie (STOC 2016) by incorporating new insights and simplifying several steps. Overall, this yields an easier to grasp procedure with lower complexity.

Connected realizations of joint-degree matrices

We study a restriction of the classic degree sequence graphic realization problem studied by Erdős, Gallai, Havel, and Hakimi, namely the joint-degree matrix graphic realization problem. Here, in addition to the degree sequence, a joint degree matrix is given, the (i,j)th element of which specifies the exact number of edges between vertices of degree di and vertices of degree dj. The decision and construction versions of the problem have a relatively straightforward solution. In this work, however, we focus on the corresponding connected graphic realization version of the problem. We give a necessary and sufficient condition for a connected graphic realization to exist, as well as a polynomial time construction algorithm that involves a novel recursive search of suitable local graph modifications. As a byproduct, we also suggest an alternative polynomial time algorithm for the joint-degree matrix graphic realization problem that never increases the number of connected components of the graph constructed.

On Budget-Feasible Mechanism Design for Symmetric Submodular Objectives

We study a class of procurement auctions with a budget constraint, where an auctioneer is interested in buying resources from a set of agents. The auctioneer would like to select a subset of the resources so as to maximize his valuation function, without exceeding his budget. As the resources are owned by strategic agents, our overall goal is to design mechanisms that are truthful, budget-feasible, and obtain a good approximation to the optimal value. Previous results on budget-feasible mechanisms have considered mostly monotone valuation functions. In this work, we mainly focus on symmetric submodular valuations, a prominent class of non-monotone submodular functions that includes cut functions. We begin with a purely algorithmic result, obtaining a \(\frac{2e}{e-1}\)-approximation for maximizing symmetric submodular functions under a budget constraint. We then proceed to propose truthful, budget feasible mechanisms (both deterministic and randomized), paying particular attention on the Budgeted Max Cut problem. Our results significantly improve the known approximation ratios for these objectives, while establishing polynomial running time for cases where only exponential mechanisms were known. At the heart of our approach lies an appropriate combination of local search algorithms with results for monotone submodular valuations, applied to the derived local optima.

Inequity Aversion Pricing over Social Networks: Approximation Algorithms and Hardness Results.

We study a revenue maximization problem in the context of social networks. Namely, we consider a model introduced by Alon, Mansour, and Tennenholtz (EC 2013) that captures inequity aversion, i.e., prices offered to neighboring vertices should not be significantly different. We first provide approximation algorithms for a natural class of instances, referred to as the class of single-value revenue functions. Our results improve on the current state of the art, especially when the number of distinct prices is small. This applies, for example, to settings where the seller will only consider a fixed number of discount types or special offers. We then resolve one of the open questions posed in Alon et al., by establishing APX-hardness for the problem. Surprisingly, we further show that the problem is NP-complete even when the price differences are allowed to be large, or even when the number of allowed distinct prices is as small as three. Finally, we provide some extensions of the model, regarding either the allowed set of prices or the demand type of the clients.