Michael Schapira

An improved approximation algorithm for combinatorial auctions with submodular bidders

We explore the allocation problem in combinatorial auctions with submodular bidders. We provide an e/e-1 approximation algorithm for this problem. Moreover, our algorithm applies to the more general class of XOS bidders. By presenting a matching unconditional lower bound in the communication model, we prove that the upper bound is tight for the XOS class.Our algorithm improves upon the previously known 2-approximation algorithm. In fact, we also exhibit another algorithm which obtains an approximation ratio better than 2 for submodular bidders, even in the value queries model.Throughout the paper we highlight interesting connections between combinatorial auctions with XOS and submodular bidders and various other combinatorial optimization problems. In particular, we discuss coverage problems and online problems.

Truthful randomized mechanisms for combinatorial auctions

We present a new framework for the design of computationally-efficient and incentive-compatible mechanisms for combinatorial auctions. The mechanisms obtained via this framework are randomized, and obtain incentive compatibility in the universal sense (in contrast to the substantially weaker notion of incentive compatibility in expectation). We demonstrate the usefulness of our techniques by exhibiting two mechanisms for combinatorial auctions with general bidder preferences. The first mechanism obtains an optimal O(m)-approximation to the optimal social welfare for arbitrary bidder valuations. The second mechanism obtains an O(log^2m)-approximation for a class of bidder valuations that contains the important class of submodular bidders. These approximation ratios greatly improve over the best (known) deterministic incentive-compatible mechanisms for these classes.

Bayesian Combinatorial Auctions

We study the following Bayesian setting: mitems are sold to nselfish bidders in mindependent second-price auctions. Each bidder has a privatevaluation function that expresses complex preferences over allsubsets of items. Bidders only have beliefsabout the valuation functions of the other bidders, in the form of probability distributions. The objective is to allocate the items to the bidders in a way that provides a good approximation to the optimal social welfare value. We show that if bidders have submodular valuation functions, then every Bayesian Nash equilibrium of the resulting game provides a 2-approximation to the optimal social welfare. Moreover, we show that in the full-information game a pure Nash always exists and can be found in time that is polynomial in both mand n.

On the Hardness of Being Truthful

The central problem in computational mechanism design is the tension between incentive compatibility and computational efficiency. We establish the first significant approximability gap between algorithms that are both truthful and computationally-efficient, and algorithms that only achieve one of these two desiderata. This is shown in the context of a novel mechanism design problem which we call the combinatorial public project problem (cppp). cpppis an abstraction of many common mechanism design situations, ranging from elections of kibbutz committees to network design.Our result is actually made up of two complementary results -- one in the communication-complexity model and one in the computational-complexity model. Both these hardness results heavily rely on a combinatorial characterization of truthful algorithms for our problem. Our computational-complexity result is one of the first impossibility results connecting mechanism design to complexity theory; its novel proof technique involves an application of the Sauer-Shelah Lemma and may be of wider applicability, both within and without mechanism design.

Approximation Algorithms for Combinatorial Auctions with Complement-Free Bidders

In a combinatorial auction m heterogenous indivisible items are sold to n bidders. This paper considers settings in which the valuation functions of the bidders are known to be complement free (a.k.a. subadditive). We provide several approximation algorithms for the social-welfare maximization problem in such settings. First, we present a logarithmic upper bound for the case that the access to the valuation functions is via demand queries. For the weaker value queries model we provide a tight O(√m) approximation. Unlike the other algorithms we present, this algorithm is also incentive compatible. Finally, we present two approximation algorithms for the more restricted class of XOS valuations: A simple deterministic algorithm that provides an approximation ratio of two and an optimal e/(e -1) approximation achieved via randomized rounding. We also present optimal lower bounds for both the demand oracles model and the value oracles model.

A survey of interdomain routing policies

Researchers studying the inter-domain routing system typically rely on models to fill in the gaps created by the lack of information about the business relationships and routing policies used by individual autonomous systems. To shed light on this unknown information, we asked 100 network operators about their routing policies, billing models, and thoughts on routing security. This short paper reports the surveys results and discusses their implications.

A new approach to interdomain routing based on secure multi-party computation

Interdomain routing involves coordination among mutually distrustful parties, leading to the requirements that BGP provide policy autonomy, flexibility, and privacy. BGP provides these properties via the distributed execution of policy-based decisions during the iterative route computation process. This approach has poor convergence properties, makes planning and failover difficult, and is extremely difficult to change. To rectify these and other problems, we propose a radically different approach to interdomain-route computation, based on secure multi-party computation (SMPC). Our approach provides stronger privacy guarantees than BGP and enables the deployment of new policy paradigms. We report on an initial exploration of this idea and outline future directions for research.

Computation and incentives in combinatorial public projects

The Combinatorial Public Projects Problem (CPPP) is an abstraction of resource allocation problems in which agents have preferences over alternatives, and an outcome that is to be collectively shared by the agents is chosen so as to maximize the social welfare. We explore CPPP from both computational perspective and a mechanism design perspective. We examine CPPP in the hierarchy of complement free (subadditive) valuation classes and present positive and negative results for both unrestricted and truthful algorithms.

Approximate privacy: foundations and quantification (extended abstract)

Increasing use of computers and networks in business, government, recreation, and almost all aspects of daily life has led to a proliferation of online sensitive data about individuals and organizations. Consequently, concern about the privacy of these data has become a top priority, particularly those data that are created and used in electronic commerce. Despite many careful formulations and extensive study, there are still open questions about the feasibility of maintaining meaningful privacy in realistic networked environments. We formulate communication-complexity-based definitions, both worst-case and average-case, of a problems privacy-approximation ratio. We use our definitions to investigate the extent to which approximate privacy is achievable in many well studied contexts: the 2ndprice Vickrey auction [20], the millionaires problem of Yao [22], the provisioning of a public good, and also set disjointness and set intersection. We present both positive and negative results and many interesting directions for future research.

Modeling on quicksand: dealing with the scarcity of ground truth in interdomain routing data

Researchers studying the interdomain routing system, its properties and new protocols, face many challenges in performing realistic evaluations and simulations. Modeling decisions with respect to AS-level topology, routing policies and traffic matrices are complicated by a scarcity of ground truth for each of these components. Moreover, scalability issues arise when attempting to simulate over large (although still incomplete) empirically-derived AS-level topologies. In this paper, we discuss our approach for analyzing the robustness of our results to incomplete empirical data. We do this by (1) developing fast simulation algorithms that enable us to (2) running multiple simulations with varied parameters that test the sensitivity of our research results.