Nicholas J. A. Harvey

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Scalable overlay networks such as Chord, CAN, Pastry, and Tapestry have recently emerged as flexible infrastructure for building large peer-to-peer systems. In practice, such systems have two disadvantages: They provide no control over where data is stored and no guarantee that routing paths remain within an administrative domain whenever possible. SkipNet(More)
We consider information networks in the absence of interference and noise, and present an upper bound on the rate at which information can be transmitted using network coding. Our upper bound is based on combining properties of entropy with a strong information inequality derived from the structure of the network.The <b>undirected</b> <i>k</i>-<b>pairs(More)
Submodular functions are a key concept in combinatorial optimization. Algorithms that involve submodular functions usually assume that they are given by a (value) oracle. Many interesting problems involving submodular functions can be solved using only polynomially many queries to the oracle, e.g., exact minimization or approximate maximization. In this(More)
We present a new deterministic algorithm to construct network codes for multicast problems, a particular class of network information ow problems. Our algorithm easily generalizes to several variants of multicast problems. Our approach is based on a new algorithm for <i>maximum-rank completion of mixed matrices</i>---taking a matrix whose entries are a(More)
We consider the problem of fairly matching the left-hand vertices of a bipartite graph to the right-hand vertices. We refer to this problem as the optimal semimatching problem; it is a relaxation of the known bipartite matching problem. We present a way to evaluate the quality of a given semi-matching and show that, under this measure, an optimal(More)
We give near-optimal sketching and streaming algorithms for estimating Shannon entropy in the most general streaming model, with arbitrary insertions and deletions. This improves on prior results that obtain suboptimal space bounds in the general model, and near-optimal bounds in the insertion-only model without sketching. Our high-level approach is simple:(More)
We present new algebraic approaches for several well-known combinatorial problems, including non-bipartite matching, matroid intersection, and some of their generalizations. Our work yields new randomized algorithms that are the most efficient known. For non-bipartite matching, we obtain a simple, purely algebraic algorithm with running time O(n) where n is(More)