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We consider the problem of maximizing a nonnegative (possibly non-monotone) submodular set function with or without constraints. Feige et al. [9] showed a 2/5-approximation for the unconstrained problem and also proved that no approximation better than 1/2 is possible in the value oracle model. Constant-factor approximation has been also known for… (More)

We consider the Asymmetric Traveling Salesman problem for costs satisfying the triangle inequality. We derive a ran-domized algorithm which delivers a solution within a factor O(log n/ log log n) of the optimum with high probability.

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 0 , we give a (3 2 − 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 the… (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 φ(G) be the minimum conductance of an undirected graph G, and let 0=λ<sub>1</sub> ≤ λ<sub>2</sub> ≤ ... ≤ λ<sub>n</sub> ≤ 2 be the eigenvalues of the normalized Laplacian matrix of G. We prove that for any graph G and any k ≥ 2, [φ(G) = O(k) l<sub>2</sub>/√l<sub>k</sub>,] and this performance… (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)

We give a constant factor approximation algorithm for the asymmetric traveling salesman problem when the support graph of the solution of the Held-Karp linear programming relaxation has bounded orientable genus.

We present a number of positive and negative results for variants of the matroid secretary problem. Most notably, we design a constant-factor competitive algorithm for the “random assignment” model where the weights are assigned randomly to the elements of a matroid, and then the elements arrive on-line in an adversarial order (extending a result of Soto,… (More)

We introduce a simple benchmark model of dynamic matching in networked markets, where agents arrive and depart stochastically and the network of acceptable transactions between agents forms a random graph. We analyze our model from three perspectives: waiting time, optimization, and information. The main insight of our analysis is that waiting to thicken… (More)