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We consider the online stochastic matching problem proposed by Feldman et al. [4] as a model of display ad allocation. We are given a bipartite graph; one side of the graph corresponds to a fixed set of bins and the other side represents the set of possible ball types. At each time step, a ball is sampled independently from the given distribution and it(More)
For some positive constant \eps_0, we give a (3/2-\eps_0)-approximation algorithm for the following problem: given a graph G_0=(V,E_0), find the shortest tour that visits every vertex at least once. This is a special case of the metric traveling salesman problem when the underlying metric is defined by shortest path distances in G_0. The result improves on(More)
A basic fact in spectral graph theory is that the number of connected components in an undirected graph is equal to the multiplicity of the eigenvalue zero in the Laplacian matrix of the graph. In particular, the graph is disconnected if and only if there are at least two eigenvalues equal to zero. Cheeger's inequality and its variants provide an(More)
Let &#966;(G) be the minimum conductance of an undirected graph G, and let 0=&#955;<sub>1</sub> &#8804; &#955;<sub>2</sub> &#8804; ... &#8804; &#955;<sub>n</sub> &#8804; 2 be the eigenvalues of the normalized Laplacian matrix of G. We prove that for any graph G and any k &#8805; 2, [&#966;(G) = O(k) l<sub>2</sub>/&#8730;l<sub>k</sub>,] and this performance(More)
We prove a structure theorem for the feasible solutions of the Arora-Rao-Vazirani SDP relaxation on low threshold rank graphs and on small-set expanders. We show that if G is a graph of bounded threshold rank or a small-set expander, then an optimal solution of the Arora-Rao-Vazirani relaxation (or of any stronger version of it) can be almost entirely(More)
We give approximation algorithms and inapproximability results for a class of movement problems. In general, these problems involve planning the coordinated motion of a large collection of objects (representing anything from a robot swarm or firefighter team to map labels or network messages) to achieve a global property of the network while minimizing the(More)
Spectral partitioning is a simple, nearly-linear time, algorithm to find sparse cuts, and the Cheeger inequalities provide a worst-case guarantee of the quality of the approximation found by the algorithm. Local graph partitioning algorithms [1], [2], [3] run in time that is nearly linear in the size of the output set, and their approximation guarantee is(More)