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There are two main algorithmic approaches to sparse signal recovery: geometric and combinatorial. The geometric approach utilizes geometric properties of the measurement matrix Phi. A notable example is the Restricted Isometry Property, which states that the mapping Phi preserves the Euclidean norm of sparse signals; it is known that random dense matrices(More)
In recent years the MapReduce framework has emerged as one of the most widely used parallel computing platforms for processing data on terabyte and petabyte scales. Used daily at companies such as Yahoo!, Google, Amazon, and Facebook, and adopted more recently by several universities, it allows for easy parallelization of data intensive computations over(More)
We prove that if a linear error-correcting code C : f0;1g n ! f0;1g m is such that a bit of the message can be probabilistically reconstructed by looking at two entries of a corrupted codeword, then m = 2 (n). We also present several extensions of this result. We show a reduction from the complexity of one-round, information-theoretic Private Information(More)
We consider the on-line version of the original <italic>m</italic>-machine scheduling problem: given <italic>m</italic> machines and <italic>n</italic> positive real jobs, schedule the <italic>n</italic> jobs on the <italic>m</italic> machines so as to minimize the makespan, the completion time of the last job. In the on-line version, as soon as job(More)
In the 0-<i>extension problem</i>, we are given a weighted graph with some nodes marked as <i>terminals</i> and a semi-metric on the set of terminals. Our goal is to assign the rest of the nodes to terminals so as to minimize the sum, over all edges, of the product of the edge's weight and the distance between the terminals to which its endpoints are(More)
We describe a randomized approximation algorithm which takes an instance of MAX 3SAT as input. If the instance—a collection of clauses each of length at most three—is satisfi-able, then the expected weight of the assignment found is at least 7=8 of optimal. We provide strong evidence (but not a proof) that the algorithm performs equally well on arbitrary(More)
We study the problem of nding a most prootable subset of n given tasks, each with a given start and nish time as well as proot and resource requirement, that at no time exceeds the quantity B of available resource. We show that this NP-hard Resource Allocation problem can be (1=2?")-approximated in polynomial time, which improves upon earlier approximation(More)
We consider the on-line version of the original m-machine scheduling problem: given m machines and n positive real jobs, schedule the n jobs on the m machines so as to minimize the makespan, the completion time of the last job. In the on-line version, as soon as a job arrives, it must be assigned immediately to one of the m machines. We study the(More)