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Provisioning a virtual private network: a network design problem for multicommodity flow
This work establishes a relation between this collection of network design problems and a variant of the facility location problem introduced by Karger and Minkoff, and provides optimal and approximate algorithms for several variants of this problem, depending on whether the traffic matrix is required to be symmetric. Expand
Primal–Dual Algorithms for Connected Facility Location Problems
The first primal–dual algorithms for these problems are given and achieve the best known approximation guarantees and the results were not combinatorial—they were obtained by solving an exponential size linear rogramming relaxation. Expand
Clustering with Spectral Norm and the k-Means Algorithm
  • Amit Kumar, R. Kannan
  • Mathematics, Computer Science
  • IEEE 51st Annual Symposium on Foundations of…
  • 11 April 2010
This paper shows that a simple clustering algorithm works without assuming any generative (probabilistic) model, and proves some new results for generative models - e.g., it can cluster all but a small fraction of points only assuming a bound on the variance. Expand
Maximum Coverage Problem with Group Budget Constraints and Applications
MCG is used to obtain the first constant factor approximation algorithms for the following problems: (i) multiple depot k-traveling repairmen problem with covering constraints and (ii) orienteering problem with time windows when the number of time windows is a constant. Expand
Algorithms for provisioning virtual private networks in the hose model
Novel algorithms for provisioning VPNs in the hose model are developed and it is shown that the VPN trees constructed by the proposed algorithms dramatically reduce bandwidth requirements compared to scenarios in which Steiner trees are employed to connect VPN endpoints. Expand
Resource augmentation for weighted flow-time explained by dual fitting
A general dual-fitting technique for analyzing online scheduling algorithms in the unrelated machines setting where the objective function involves weighted flow-time, and it is proposed that one can often analyze such algorithms by looking at the dual of the linear program for the corresponding scheduling problem, and finding a feasible dual solution as the on-line algorithm proceeds. Expand
Deterministic wavelet thresholding for maximum-error metrics
This paper introduces an optimal low polynomial-time algorithm for one-dimensional wavelet thresholding, based on a new Dynamic-Programming (DP) formulation, and can be employed to minimize the maximum relative or absolute error in the data reconstruction. Expand
Simpler and better approximation algorithms for network design
A simple and easy-to-analyze randomized approximation algorithms for several well-studied NP-hard network design problems and a simple constant-factor approximation algorithm for the single-sink buy-at-bulk network design problem. Expand
A simple linear time (1 + /spl epsiv/)-approximation algorithm for k-means clustering in any dimensions
We present the first linear time (1 + /spl epsiv/)-approximation algorithm for the k-means problem for fixed k and /spl epsiv/. Our algorithm runs in O(nd) time, which is linear in the size of theExpand
Connectivity and inference problems for temporal networks
This work defines and studies the class of inference problems, in which it seeks to reconstruct a partially specified time labeling of a network in a manner consistent with an observed history of information flow, and provides results on two types of problems for temporal networks. Expand