Market Equilibrium in Exchange Economies with Some Families of Concave Utility Functions

We present explicit convex programs which characterize the equilibrium for certain additively separable utility functions and CES functions. These include some CES utility functions that do not satisfy weak gross substitutability.Exchange economy, computation of equilibria, convex feasibility problem

Ubicrawler: a scalable fully distributed web crawler

We present the design and implementation of UbiCrawler, a scalable distributed web crawler, and we analyze its performance. The main features of UbiCrawler are platform independence, fault tolerance, a very effective assignment function for partitioning the domain to crawl, and more in general the complete decentralization of every task

Computation of the Lovasz Theta Function for Circulant Graphs

The Lovasz theta function (G) of a graph G has attracted a lot of attention for its connection with diverse issues, such as communicating without errors and computing large cliques in graphs. Indeed this function enjoys the remarkable property of being computable in polynomial time, despite being sandwitched between clique and chromatic number, two well known hard to compute quantities. In this paper we deal with the computation of the Lovasz function of certain circulant graphs, i.e., graphs whose adjacency matrix is circulant. Such graphs are important for both theoretical and practical reasons, and indeed arise in many dierent contests. The simplest circulant graph is the cycle; for the cycle, Lovasz showed a simple formula expressing the value of the theta function. We consider the theta function of circulant graphs which can be viewed as the super-position of two cycles, i.e., circulant graphs of degree 4. We invertigate the possibility to take advantage of the specis structure of the circulants in oreder to achieve higher eciency. For a circulant graph Cn;j on n vertices and with a chord length j, 2 j bn=2c, we propose an O(j) time algorithm to compute (Cn;j ) if j is odd and an O(n=j) time algorithm if j is even. This is a signicant improvement over the best known algorithms for the theta function computation for general graphs which take O(n4) time. We also derive conditions under which (Cn;j ) can be computed in O(1) time

A fast and stable parallel QR algorithm for symmetric tridiagonal matrices

AbstractWe present a new, fast, and practical parallel algorithm for computing a few eigenvalues of a symmetric tridiagonal matrix by the explicitQR method. We present a new divide and conquer parallel algorithm which is fast and numerically stable. The algorithm is work efficient and of low communication overhead, and it can be used to solve very large problems infeasible by sequential methods

Small Worlds

In this tutorial we present some basic ideas behind the notion of Small World. We review the state-of-the-art in the field, and put emphasis on some recent developments, in connection with analyzing the structure of the Web.-

Generating Realistic Data Sets for Combinatorial Auctions

We consider the generation of realistic data sets for combinatorial auctions. This problem has been recognized as central to enhance the contribution of the computer science community to the field. We put forward the notions of structure and budget as main guidelines towards the generation of succinct and realistic input data. We describe a computational framework for the analysis of existing algorithms against realistic benchmarks, and use it in the context of two real world scenarios, i.e., real estate and railroad track auctions. The results of this analysis suggest that the obstacles to using (one round) combinatorial auctions in real world applications might be of an economic nature rather than a computational one

On the hardness of approximating the permanent of structured matrices

We show that for several natural classes of "structured" matrices, including symmetric, circulant, Hankel and Toeplitz matrices, approximating the permanent modulo a prime p is as hard as computing its exact value. Results of this kind are well known for arbitrary matrices. However the techniques used do not seem to apply to "structured" matrices. Our approach is based on recent advances in the hidden number problem introduced by Boneh and Venkatesan in 1996 combined with some bounds of exponential sums motivated by the Waring problem in finite fields

Computing Equilibrium in Matching Markets

Market equilibria of matching markets offer an intuitive and fair solution for matching problems without money with agents who have preferences over the items. Such a matching market can be viewed as a variation of Fisher market, albeit with rather peculiar preferences of agents. These preferences can be described by piece-wise linear concave (PLC) functions, which however, are not separable (due to each agent only asking for one item), are not monotone, and do not satisfy the gross substitute property-- increase in price of an item can result in increased demand for the item. Devanur and Kannan in FOCS 08 showed that market clearing prices can be found in polynomial time in markets with fixed number of items and general PLC preferences. They also consider Fischer markets with fixed number of agents (instead of fixed number of items), and give a polynomial time algorithm for this case if preferences are separable functions of the items, in addition to being PLC functions. Our main result is a polynomial time algorithm for finding market clearing prices in matching markets with fixed number of different agent preferences, despite that the utility corresponding to matching markets is not separable. We also give a simpler algorithm for the case of matching markets with fixed number of different items