The function ∑n i=1 cixi is known as the objective function, and the m inequalities are known as constraints; the coefficient matrix of the linear program is the m× n matrix A whose entries are aji.Expand

This work investigates variants of Lloyd's heuristic for clustering high dimensional data in an attempt to explain its popularity (a half century after its introduction) among practitioners, and proposes and justifies a clusterability criterion for data sets.Expand

A new linear programming relaxation for Multiway Cut is presented and a new approximation algorithm based on it achieves a performance ratio of at most 1.5?1k, which improves the previous result for every value of k.Expand

Significantly improving and extending recent results of Kleinberg, data structures whose size is polynomial in the size of the database and search algorithms that run in time nearly linear or nearly quadratic in the dimension are constructed.Expand

It is shown that the minimum cut ratio is within a factor of O(log k) of the maximum concurrent flow for k-commodity flow instances with arbitrary capacities and demands, and thus of the optimal min-cut ratio.Expand

This work develops a general technique for the quantitative analysis of iterative distributed load balancing schemes, and applies this technique to obtain bounds on the number of rounds required to achieve coarse balancing in general networks, cycles and meshes in these models.Expand

It is proved that the integrality ratio of the metric relaxation is at least c√lgk for a positive c for infinitely many k and the results improve some of the results of Kleinberg and Tardos and they further the understanding on how to use metric relaxations.Expand

This work considers the ploying all optica P roblem of routing in networks emrouting technology, and shows any permutation can be routed efficiently in one round using at most 0(log2n/P2) wavelengths, where p is the edge expansion of the network.Expand

We deal with the competitive analysis of algorithms for managing data in a distributed environment. We deal with the file allocation problem, where copies of a file may be be stored in the local… Expand

This paper undertake the first study of statistical multiplexing from the perspective of approximation algorithms, and considers one of the most commonly studied models: that of two communicating nodes connected by a set of parallel edges, where the rate of each connection between them is a random variable.Expand