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A unified framework for approximating and clustering data
A unified framework for constructing coresets and approximate clustering for general sets of functions, and shows how to generalize the results of the framework for squared distances, distances to the qth power, and deterministic constructions. Expand
Resilient network coding in the presence of Byzantine adversaries
This paper introduces the first distributed polynomial-time rate-optimal network codes that work in the presence of Byzantine nodes, and presents algorithms that target adversaries with different attacking capabilities. Expand
Approximation Algorithms for Maximization Problems Arising in Graph Partitioning
It is shown that if a graph has a vertex cover of size k, then one can select in polynomial time a set of k vertices that covers over 80% of the edges. Expand
Network Codes Resilient to Jamming and Eavesdropping
This paper provides polynomial-time distributed network codes that are information-theoretically rate-optimal for this scenario, improving on the rates achievable in prior work by Ngai and corrects an error by a subset of the authors. Expand
The RPR2 rounding technique for semidefinite programs
This work shows that the random hyperplane rounding technique introduced by Goemans and Williamson, and its variant that involves outward rotation, are both special cases of RPR2, and improves the tradeoff curve that relates the approximation ratio to the size of the maximum cut in a graph. Expand
Universal ε-approximators for integrals
Let <i>X</i> be a space and <i>F</i> a family of 0, 1-valued functions on <i>X</i>. Vapnik and Chervonenkis showed that if <i>F</i> is "simple" (finite VC dimension), then for every probabilityExpand
Private codes or succinct random codes that are (almost) perfect
  • M. Langberg
  • Mathematics, Computer Science
  • 45th Annual IEEE Symposium on Foundations of…
  • 17 October 2004
This work presents private codes in which the size of the joint random string is O(log n) and establishes a connection between list decodable codes and private codes which complements a recent result of Guruswami (CCC '03) on list decoding with side information. Expand
The encoding complexity of network coding
It is proved that in an acyclic coding network, the number of encoding nodes required to achieve the capacity of the network is bounded h3k2, where B is the minimum size of the feedback link set. Expand
The multi-multiway cut problem
This paper presents an approximation algorithm for the multi-multiway cut problem with an approximation ratio which matches that obtained by Garg, Vazirani, and Yannakakis on the standard multicut problem and improves the O(logLPloglogLP) approximation ratio for the minimumMulticut problem. Expand
Local graph coloring and index coding
A novel upper bound for the optimal index coding rate is presented, using a graph theoretic quantity called the local chromatic number and it is shown how a good local coloring can be used to create a good index code. Expand