VirtualShave is a novel tool to remove hair from digital dermatoscopic images. First, individual hairs are identified using a top-hat filter followed by morphological postprocessing. Then, they are replaced through PDE-based inpainting with an estimate of the underlying occluded skin. VirtualShave's performance is comparable to that of a human operator removing hair manually, and the resulting images are almost indistinguishable from those of hair-free skin.

Oblivious RAM (ORAM), first introduced in the ground-breaking work of Goldreich and Ostrovsky (STOC ’87 and J. ACM ’96) is a technique for provably obfuscating programs’ access patterns, such that the access patterns leak no information about the programs’ secret inputs. To compile a general program to an oblivious counterpart, it is well-known that amortized blowup is necessary, where N is the size of the logical memory. This was shown in Goldreich and Ostrovksy’s original ORAM work for statistical security and in a somewhat restricted model (the so called balls-and-bins model), and recently by Larsen and Nielsen (CRYPTO ’18) for computational security. A long standing open question is whether there exists an optimal ORAM construction that matches the aforementioned logarithmic lower bounds (without making large memory word assumptions, and assuming a constant number of CPU registers). In this paper, we resolve this problem and present the first secure ORAM with amortized blowup, assuming one-way functions. Our result is inspired by and non-trivially improves on the recent beautiful work of Patel et al. (FOCS ’18) who gave a construction with amortized blowup, assuming one-way functions. One of our building blocks of independent interest is a linear-time deterministic oblivious algorithm for tight compaction: Given an array of n elements where some elements are marked, we permute the elements in the array so that all marked elements end up in the front of the array. Our O ( n ) algorithm improves the previously best known deterministic or randomized algorithms whose running time is or , respectively.

This paper investigates some computational problems associated with probabilistic translation models that have recently been adopted in the literature on machine translation. These models can be viewed as pairs of probabilistic contextfree grammars working in a 'synchronous' way. Two hardness results for the class NP are reported, along with an exponential time lower-bound for certain classes of algorithms that are currently used in the literature.

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We study the complexity of local graph centrality estimation, with the goal of approximating the centrality score of a given target node while exploring only a sublinear number of nodes/arcs of the graph and performing a sublinear number of elementary operations. We develop a technique, that we apply to the PageRank and Heat Kernel centralities, for building a low-variance score estimator through a local exploration of the graph. We obtain an algorithm that, given any node in any graph of m arcs, with probability (1 − δ) computes a multiplicative (1±ǫ)-approximation of its score by examining onlyÕ min m 2/3 ∆ 1/3 d −2/3 , m 4/5 d −3/5 nodes/arcs, where ∆ and d are respectively the maximum and average outdegree of the graph (omitting for readability poly(ǫ −1 ) and polylog(δ −1 ) factors). A similar bound holds for computational complexity. We also prove a lower bound of Ω min m 1/2 ∆ 1/2 d −1/2 , m 2/3 d −1/3 for both query complexity and computational complexity. Moreover, our technique yields aÕ(n 2/3 ) query complexity algorithm for the graph access model of Brautbar et al. [14], widely used in social network mining; we show this algorithm is optimal up to a sublogarithmic factor. These are the first algorithms yielding worst-case sublinear bounds for general directed graphs and any choice of the target node. * This is the full version of a paper accepted for publication at IEEE FOCS 2018. IntroductionComputing graph centralities efficiently is essential to modern network analysis. With the advent of web and social networks, the prototypical scenario involves massive graphs on millions or even billions of nodes and arcs. On these inputs graphs, traditional approaches such as Monte Carlo simulations and algebraic techniques are often impractical -if not entirely useless -since their cost can scale linearly or superlinearly with the size of the graph. An alternative approach is that of local graph algorithms, that, broadly speaking, work by exploring only a small portion of the graph around a given target node. Local algorithms are justified by the fact that, often, one does not need an exact computation of the entire score vector, but only a quick approximation for a few nodes of interest. Obviously, in exchange one hopes to drastically reduce both the running time and the portion of the graph to be fetched. One of the best-known examples is perhaps local graph clustering [4,54,33].In this paper we address the problem of locally approximating the centrality score of a node in a graph, focusing on the PageRank and heat kernel centralities. PageRank [20] is a classic graph centrality measure with a vast number of applications including local graph clustering [4], trendsetter identification [52], spam filtering [40], link prediction [39] and many more (see [35] and [23]); it has been named one of the top 10 algorithms in data mining [55]. Heat kernel [24] can be seen as a variant of PageRank that satisfies the heat equation. Its applications span biological network analysis [31,30] and solving local linear systems...