Vijay V. Vazirani

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We present approximation algorithms for the metric uncapacitated facility location problem and the metric <italic>k</italic>-median problem achieving guarantees of 3 and 6 respectively. The distinguishing feature of our algorithms is their low running time: <italic>O(m</italic> log<italic>m</italic>) and <italic>O(m</italic> log<italic>m(L</italic> + log(More)
There has been a great deal of interest recently in the relative power of on-line and off-line algorithms. An on-line algorithm receives a sequence of requests and must respond to each request as soon as it is receiveD. An off-line algorithm may wait until all requests have been received before determining its responses. One approach to evaluating an(More)
A new algorithm for finding a maximum matching in a general graph is presented; its special feature being that the only computationally non-trivial step required in its execution is the inversion of a single integer matrix. Since this step can be parallelized, we get a simple parallel (RNC2) algorithm. At the heart of our algorithm lies a probabilistic(More)
Consider the multicommodity flow problem in which the object is to maximize the sum of commodities routed. We prove the following approximate max-flow min-multicut theorem: min multicut O(log k) ~ max flow ~ min multicut, where k is the number of commodities. Our proof is constructive; it enables us to find a multicut within O(log k) of the max flow (and(More)
In this article, we will formalize the method of dual fitting and the idea of factor-revealing LP. This combination is used to design and analyze two greedy algorithms for the metric uncapacitated facility location problem. Their approximation factors are 1.861 and 1.61, with running times of <i>O</i>(<i>m</i> log <i>m</i>) and(More)
How does a search engine company decide what ads to display with each query so as to maximize its revenue&quest; This turns out to be a generalization of the online bipartite matching problem. We introduce the notion of a trade-off revealing LP and use it to derive an optimal algorithm achieving a competitive ratio of 1&minus;1/<i>e</i> for this problem.
We study the maximum integral multicommodity flow problem and the minimum multicut problem restricted to trees. This restriction is quite rich and contains as special cases classical optimization problems such as matching and vertex cover for general graphs. It is shown that both the maximum integral multicommodity flow and the minimum multicut problem are(More)