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We introduce several generalizations of classical computer science problems obtained by replacing simpler objective functions with general submodular functions. The new problems include submodular load balancing, which generalizes load balancing or minimum-makespan scheduling, submodular sparsest cut and submodular balanced cut, which generalize their… (More)

A common approach for dealing with large datasets is to stream over the input in one pass, and perform computations using sublinear resources. For truly massive datasets, however, even making a single pass over the data is prohibitive. Therefore, streaming computations must be distributed over many machines. In practice, obtaining significant speedups using… (More)

We consider the facility location problem with hierarchical facility costs, and give a (4.236 + ε)-approximation algorithm using local search. The hierarchical facility location problem models multilevel service installation costs. Shmoys, Swamy and Levi [13] gave an approximation algorithm for a two-level version of the problem. Here we consider a… (More)

We study the lower-bounded facility location problem which generalizes the classical uncapacitated facility location problem in that it comes with lower bound constraints for the number of clients assigned to a facility in the case that this facility is opened. This problem was introduced independently in the papers by Karger and Minkoff [2000] and by Guha… (More)

We introduce the Minimum-size bounded-capacity cut (MinSBCC) problem, in which we are given a graph with an identified source and seek to find a cut minimizing the number of nodes on the source side, subject to the constraint that its capacity not exceed a prescribed bound B. Besides being of interest in the study of graph cuts, this problem arises in many… (More)

Internet search companies sell advertisement slots based on users' search queries via an auction. Advertisers have to solve a complex optimization problem of how to place bids on the keywords of their interest so that they can maximize their return (the number of user clicks on their ads) for a given budget. This is the budget optimization problem. In this… (More)

We propose the Min-max multiway cut problem, a variant of the traditional Multiway cut problem, but with the goal of minimizing the maximum capacity (rather than the sum or average capacity) leaving a part of the partition. The problem is motivated by data partitioning in Peer-to-Peer networks. The min-max objective function forces the solution not to… (More)

We introduce and study a combinatorial problem called preference-constrained oriented matching. This problem is defined on a directed graph in which each node has preferences over its out-neighbors, and the goal is to find a maximum-size matching on this graph that satisfies a certain preference constraint. One of our main results is a structural theorem… (More)

We study integrality gaps and approximability of two closely related problems on directed graphs. Given a set <i>V</i> of <i>n</i> nodes in an underlying asymmetric metric and two specified nodes <i>s</i> and <i>t</i>, both problems ask to find an <i>s-t</i> path visiting all other nodes. In the <i>asymmetric traveling salesman path problem</i> (ATSPP), the… (More)