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- Sanjoy Dasgupta, Anupam Gupta
- Random Struct. Algorithms
- 2003

A result of Johnson and Lindenstrauss [13] shows that a set of n points in high dimensional Euclidean space can be mapped into an O(log n/⑀ 2)-dimensional Euclidean space such that the distance between any two points changes by only a factor of (1 Ϯ ⑀). In this note, we prove this theorem using elementary probabilistic techniques.

- Anupam Gupta, Jon M. Kleinberg, Amit Kumar, Rajeev Rastogi, Bülent Yener
- STOC
- 2001

Consider a setting in which a group of nodes, situated in a large underlying network, wishes to reserve bandwidth on which to support communication. <italic>Virtual private networks</italic> (VPNs) are services that support such a construct; rather than building a new physical network on the group of nodes that must be connected, bandwidth in the underlying… (More)

- Anupam Gupta, Robert Krauthgamer, James R. Lee
- FOCS
- 2003

The doubling constant of a metric space (X, d) is the smallest value λ such that every ball in X can be covered by λ balls of half the radius. The doubling dimension of X is then defined as dim(X) = log 2 λ. A metric (or sequence of metrics) is called doubling precisely when its doubling dimension is bounded. This is a robust class of metric spaces which… (More)

In many applications, one has to actively select among a set of expensive observations before making an informed decision. For example, in environmental monitoring, we want to select locations to measure in order to most effectively predict spatial phenomena. Often, we want to select observations which are robust against a number of possible objective… (More)

The Johnson-Lindenstrauss lemma shows that a set of n points in high dimensional Euclidean space can be mapped down into an O(log n== 2) dimensional Euclidean space such that the distance between any two points changes by only a factor of (1). In this note, we prove this lemma using elementary probabilistic techniques.

- Anupam Gupta, Martin Pál, R. Ravi, Amitabh Sinha
- STOC
- 2004

Several combinatorial optimization problems choose elements to minimize the total cost of constructing a feasible solution that satisfies requirements of clients. In the S<sc>teiner</sc> T<sc>ree</sc> problem, for example, edges must be chosen to connect terminals (clients); in V<sc>ertex</sc> C<sc>over</sc>, vertices must be chosen to cover edges… (More)

- Maria-Florina Balcan, Avrim Blum, Anupam Gupta
- SODA
- 2009

Approximation algorithms for clustering points in metric spaces is a flourishing area of research, with much research effort spent on getting a better understanding of the approximation guarantees possible for many objective functions such as k-median, k-means, and min-sum clustering. This quest for better approximation algorithms is further fueled by the… (More)

- Anupam Gupta, Amit Kumar, Tim Roughgarden
- STOC
- 2003

We give simple and easy-to-analyze randomized approximation algorithms for several well-studied NP-hard network design problems. Our algorithms improve over the previously best known approximation ratios. Our main results are the following.<ul><li>We give a randomized 3.55-approximation algorithm for the <i> connected facility location</i> problem. The… (More)

- Anupam Gupta, Katrina Ligett, Frank McSherry, Aaron Roth, Kunal Talwar
- SODA
- 2009

Consider the following problem: given a metric space, some of whose points are "clients," select a set of at most k facility locations to minimize the average distance from the clients to their nearest facility. This is just the well-studied <i>k</i>-median problem, for which many approximation algorithms and hardness results are known. Note that the… (More)

- Anupam Gupta, Amit Kumar, Martin Pál, Tim Roughgarden
- J. ACM
- 2007

We present constant-factor approximation algorithms for several widely-studied NP-hard optimization problems in network design, including the multicommodity rent-or-buy, virtual private network design, and single-sink buy-at-bulk problems. Our algorithms are simple and their approximation ratios improve over those previously known, in some cases by orders… (More)