Dimitris Paparas

Flexible use of cloud resources through profit maximization and price discrimination

Modern frameworks, such as Hadoop, combined with abundance of computing resources from the cloud, offer a significant opportunity to address long standing challenges in distributed processing. Infrastructure-as-a-Service clouds reduce the investment cost of renting a large data center while distributed processing frameworks are capable of efficiently harvesting the rented physical resources. Yet, the performance users get out of these resources varies greatly because the cloud hardware is shared by all users. The value for money cloud consumers achieve renders resource sharing policies a key player in both cloud performance and user satisfaction. In this paper, we employ microeconomics to direct the allotment of cloud resources for consumption in highly scalable master-worker virtual infrastructures. Our approach is developed on two premises: the cloud-consumer always has a budget and cloud physical resources are limited. Using our approach, the cloud administration is able to maximize per-user financial profit. We show that there is an equilibrium point at which our method achieves resource sharing proportional to each users budget. Ultimately, this approach allows us to answer the question of how many resources a consumer should request from the seemingly endless pool provided by the cloud.

The complexity of optimal multidimensional pricing

We resolve the complexity of revenue-optimal deterministic auctions in the unit-demand single-buyer Bayesian setting, i.e., the optimal item pricing problem, when the buyers values for the items are independent. We show that the problem of computing a revenue-optimal pricing can be solved in polynomial time for distributions of support size 2 and its decision version is NP-complete for distributions of support size 3. We also show that the problem remains NP-complete for the case of identical distributions.

On the Complexity of Optimal Lottery Pricing and Randomized Mechanisms

We study the optimal lottery problem and the optimal mechanism design problem in the setting of a single unit-demand buyer with item values drawn from independent distributions. Optimal solutions to both problems are characterized by a linear program with exponentially many variables. For the menu size complexity of the optimal lottery problem, we present an explicit, simple instance with distributions of support size 2, and show that exponentially many lotteries are required to achieve the optimal revenue. We also show that, when distributions have support size 2 and share the same high value, the simpler scheme of item pricing can achieve the same revenue as the optimal menu of lotteries. The same holds for the case of two items with support size 2 (but not necessarily the same high value). For the computational complexity of the optimal mechanism design problem, we show that unless the polynomial-time hierarchy collapses (more exactly, PNP = P#P), there is no universal efficient randomized algorithm to implement an optimal mechanism even when distributions have support size 3.

The Complexity of Non-Monotone Markets

We introduce the notion of non-monotone utilities, which covers a wide variety of utility functions in economic theory. We then prove that it is PPAD-hard to compute an approximate Arrow-Debreu market equilibrium in markets with linear and non-monotone utilities. Building on this result, we settle the long-standing open problem regarding the computation of an approximate Arrow-Debreu market equilibrium in markets with CES utility functions, by proving that it is PPAD-complete when the Constant Elasticity of Substitution parameter ρ is any constant less than − 1.

Clustering on k -Edge-Colored Graphs

We study the Max k-colored clustering problem, where, given an edge-colored graph with k colors, we seek to color the vertices of the graph so as to find a clustering of the vertices maximizing the number (or the weight) of matched edges, i.e. the edges having the same color as their extremities. We show that the cardinality problem is NP-hard even for edge-colored bipartite graphs with a chromatic degree equal to two and k ≥ 3. Our main result is a constant approximation algorithm for the weighted version of the Max k-colored clustering problem which is based on a rounding of a natural linear programming relaxation. For graphs with chromatic degree equal to two, we improve this ratio by exploiting the relation of our problem with the Max 2-and problem. We also present a reduction to the maximum-weight independent set (IS) problem in bipartite graphs which leads to a polynomial time algorithm for the case of two colors.

The complexity of optimal multidimensional pricing for a unit-demand buyer

Abstract We resolve the complexity of revenue-optimal deterministic auctions in the unit-demand single-buyer Bayesian setting, i.e., the optimal item pricing problem, when the buyers values for the items are independent. We show that the problem of computing a revenue-optimal pricing can be solved in polynomial time for distributions of support size 2, and its decision version is NP-complete for distributions of support size 3. We also show that the problem remains NP-complete for the case of identical distributions.

Clustering on k -edge-colored graphs

We study the Max k -colored clustering problem, where given an edge-colored graph with k colors, we seek to color the vertices of the graph so as to find a clustering of the vertices maximizing the number (or the weight) of matched edges, i.e.źthe edges having the same color as their extremities. We show that the cardinality problem is NP-hard even for edge-colored bipartite graphs with a chromatic degree equal to two and k ź 3 . Our main result is a constant approximation algorithm for the weighted version of the Max k -colored clustering problem which is based on a rounding of a natural linear programming relaxation. For graphs with chromatic degree equal to two we improve this ratio by exploiting the relation of our problem with the Max 2-and problem. We also present a reduction to the maximum-weight independent set (IS) problem in bipartite graphs which leads to a polynomial time algorithm for the case of two colors.