Howard J. Karloff

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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)
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 satisfiable, 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 MAX(More)
We prove that if a linear error-correcting code C:{0, 1} n →{0, 1} m is such that a bit of the message can be probabilistically reconstructed by looking at two entries of a corrupted codeword, then m = 2Ω (n). We also present several extensions of this result. We show a reduction from the complexity of one-round, information-theoretic Private Information(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)
Conditional functional dependencies (CFDs) have recently been proposed as a useful integrity constraint to summarize data semantics and identify data inconsistencies. A CFD augments a functional dependency (FD) with a pattern tableau that defines the context (i.e., the subset of tuples) in which the underlying FD holds. While many aspects of CFDs have been(More)
In the k-server problem, we must choose how k mobile servers will serve each of a sequence of requests, making our decisions in an online manner. We exhibit an optimai deterministic online strategy when the requests fall on the real line. For the weighted-cache problem, in which the cost of moving to + from any other point is zu(z), the weight of z, we also(More)
The celebrated semidetinite programming algorithm for MAX CUT introduced by Goemans and Williamson was known to hav; a performance ratio of at least a = — (0,87856 < cr < 0.87857); the exact per: minO<eSr ~_co~e formance ratio was unknown. We prove that the performance ratio of their algorithm is exactly a. Furthermore, we show that it is impossible to add(More)
We study the problem of finding a most profitable subset of n given tasks, each with a given start and finish time as well as profit 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−ε)-approximated in polynomial time, which improves upon earlier(More)