Clean Citation Style 002

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Fogel, Sharon; Averbuch-Elor, Hadar; Cohen, Sarel; Mazor, Shai; Litman, RoeeScrabbleGAN: Semi-Supervised Varying Length Handwritten Text Generation. Conference on Computer Vision and Pattern Recognition (CVPR) 2020: 4323-4332

Optical character recognition (OCR) systems performance have improved significantly in the deep learning era. This is especially true for handwritten text recognition (HTR), where each author has a unique style, unlike printed text, where the variation is smaller by design. That said, deep learning based HTR is limited, as in every other task, by the number of training examples. Gathering data is a challenging and costly task, and even more so, the labeling task that follows, of which we focus here. One possible approach to reduce the burden of data annotation is semi-supervised learning. Semi supervised methods use, in addition to labeled data, some unlabeled samples to improve performance, compared to fully supervised ones. Consequently, such methods may adapt to unseen images during test time. We present ScrabbleGAN, a semi-supervised approach to synthesize handwritten text images that are versatile both in style and lexicon. ScrabbleGAN relies on a novel generative model which can generate images of words with an arbitrary length. We show how to operate our approach in a semi-supervised manner, enjoying the aforementioned benefits such as performance boost over state of the art supervised HTR. Furthermore, our generator can manipulate the resulting text style. This allows us to change, for instance, whether the text is cursive, or how thin is the pen stroke.

Chechik, Shiri; Cohen, SarelDistance sensitivity oracles with subcubic preprocessing time and fast query time. Symposium Theory of Computing (STOC) 2020: 1375-1388

We present the first distance sensitivity oracle (DSO) with subcubic preprocessing time and poly-logarithmic query time for directed graphs with integer weights in the range \([−M,M]\). Weimann and Yuster [FOCS 10] presented a distance sensitivity oracle for a single vertex/edge failure with subcubic preprocessing time of \(\mathcal{O(Mn^\omega+1− \alpha})\) and subquadratic query time of \(\tilde{\mathcal{O(n^{1+\alpha})\), where \(\alpha\) is any parameter in \([0,1]\), \(n\) is the number of vertices, \(m\) is the number of edges, the \(\tilde{\mathcal{O(·)\) notation hides poly-logarithmic factors in \(n\) and \(\omega<2.373\) is the matrix multiplication exponent.Later, Grandoni and Vassilevska Williams [FOCS 12] substantially improved the query time to sublinear in \(n\). In particular, they presented a distance sensitivity oracle for a single vertex/edge failure with \(\tilde{\mathcal{O}}\)\( (Mn^\omega +1/2}\) \(+ Mn^\omega+\alpha(4−\omega)})\) preprocessing time and \(\tilde{\mathcal{O(n^{1−\alpha})\) query time. Despite the substantial improvement in the query time, it still remains polynomial in the size of the graph, which may be undesirable in many settings where the graph is of large scale. A natural question is whether one can hope for a distance sensitivity oracle with subcubic preprocessing time and very fast query time (of poly-logarithmic in \(n\)). In this paper we answer this question affirmatively by presenting a distance sensitive oracle supporting a single vertex/edge failure in subcubic \(\tilde{\mathcal{O(Mn^{2.873})\) preprocessing time for \(\omega=2.373\), \(\tilde{\mathcal{O(n^{2.5})\) space and near optimal query time of \(\tilde{\mathcal{O(1)\). For comparison, with the same \(\tilde{\mathcal{O(Mn^{2.873})\) preprocessing time the DSO of Grandoni and Vassilevska Williams has \(\tilde{\mathcal{O(n^{0.693})\) query time. In fact, the best query time their algorithm can obtain is \(\tilde{\mathcal{O(Mn^{0.385})\) (with \(\tilde{\mathcal{O(Mn^3)\) preprocessing time).

Alon, Noga; Chechik, Shiri; Cohen, SarelDeterministic Combinatorial Replacement Paths and Distance Sensitivity Oracles. International Colloquium on Automata, Languages and Programming (ICALP) 2019: 12:1-12:14

In this work we derandomize two central results in graph algorithms, replacement paths and distance sensitivity oracles (DSOs) matching in both cases the running time of the randomized algorithms. For the replacement paths problem, let \(G = (V,E)\) be a directed unweighted graph with \(n\) vertices and m edges and let \(P\) be a shortest path from \(s\) to \(t\) in \(G\). The replacement paths problem is to find for every edge \(e\) in \(P\) the shortest path from \(s\) to \(t\) avoiding \(e\). Roditty and Zwick [ICALP 2005] obtained a randomized algorithm with running time of \(\mathcal{O(m \sqrt{n})\). Here we provide the first deterministic algorithm for this problem, with the same \(\mathcal{O(m \sqrt{n})\) time. Due to matching conditional lower bounds of Williams et al. [FOCS 2010], our deterministic combinatorial algorithm for the replacement paths problem is optimal up to polylogarithmic factors (unless the long standing bound of \(\mathcal{O(mn)\) for the combinatorial boolean matrix multiplication can be improved). This also implies a deterministic algorithm for the second simple shortest path problem in \(\mathcal{O(m \sqrt{n})\) time, and a deterministic algorithm for the \(k\)-simple shortest paths problem in \(\mathcal{O(k m sqrt{n})\) time (for any integer constant \(k > 0\)). For the problem of distance sensitivity oracles, let \(G = (V,E)\) be a directed graph with real-edge weights. An \(f\)-Sensitivity Distance Oracle (\(f\)-DSO) gets as input the graph \(G=(V,E)\) and a parameter \(f\), preprocesses it into a data-structure, such that given a query \((s,t,F)\) with \(s,t \in V\) and \(F \subseteq E \cup V\), \(|F| <=f\) being a set of at most \(f\) edges or vertices (failures), the query algorithm efficiently computes the distance from \(s\) to \(t\) in the graph \(G \setminus F\) (i.e., the distance from \(s\) to \(t\) in the graph \(G\) after removing from it the failing edges and vertices \(F\)). For weighted graphs with real edge weights, Weimann and Yuster [FOCS 2010] presented several randomized \(f\)-DSOs. In particular, they presented a combinatorial \(f\)-DSO with \(\mathcal{O(mn^{4-\alpha})\) preprocessing time and subquadratic \(\mathcal{O(n^2-2(1-\alpha)/f})\) query time, giving a tradeoff between preprocessing and query time for every value of \(0 < \alpha < 1\). We derandomize this result and present a combinatorial deterministic \(f\)-DSO with the same asymptotic preprocessing and query time.

Chechik, Shiri; Cohen, SarelNear Optimal Algorithms For The Single Source Replacement Paths Problem. Symposium on Discrete Algorithms (SODA) 2019: 2090-2109

The Single Source Replacement Paths (SSRP) problem is as follows; Given a graph \(G = (V, E)\), a source vertex \(s\) and a shortest paths tree \(T_s\) rooted in \(s\), output for every vertex \(t \in V\) and for every edge \(e\) in \(T_s\) the length of the shortest path from \(s\) to \(t\) avoiding \(e\). We present near optimal upper bounds, by providing \(\tilde{\mathcal{O(m \sqrt{n} + n^2) \) time randomized combinatorial algorithm for unweighted undirected graphs, and matching conditional lower bounds for the SSRP problem.

Azar, Yossi; Cohen, SarelAn improved algorithm for online machine minimization. Operations Research Letters 2018: 128-133

The online machine minimization problem seeks to design a preemptive scheduling algorithm on multiple machines — each job \(j\) arrives at its release time \(r_j\), has to be processed for \(p_j\) time units, and must be completed by its deadline \(d_j\). The goal is to minimize the number of machines the algorithm uses. We improve the \(\mathcal{O(\log m)\)-competitive algorithm by Chen, Megow and Schewior (SODA 2016) and provide an \(\mathcal{O(\frac{\log m\log \log m})\)-competitive algorithm.

Arar, Moab; Chechik, Shiri; Cohen, Sarel; Stein, Cliff; Wajc, DavidDynamic Matching: Reducing Integral Algorithms to Approximately-Maximal Fractional Algorithms. International Colloquium on Automata, Languages and Programming (ICALP) 2018: 7:1-7:16

We present a simple randomized reduction from fully-dynamic integral matching algorithms to fully-dynamic "approximately-maximal" fractional matching algorithms. Applying this reduction to the recent fractional matching algorithm of Bhattacharya, Henzinger, and Nanongkai (SODA 2017), we obtain a novel result for the integral problem. Specifically, our main result is a randomized fully-dynamic \((2+\varepsilon)\)-approximate integral matching algorithm with small polylog worst-case update time. For the \((2+\varepsilon)\)-approximation regime only a fractional fully-dynamic \((2+\varepsilon)\)-matching algorithm with worst-case polylog update time was previously known, due to Bhattacharya et al. (SODA 2017). Our algorithm is the first algorithm that maintains approximate matchings with worst-case update time better than polynomial, for any constant approximation ratio. As a consequence, we also obtain the first constant-approximate worst-case polylogarithmic update time maximum weight matching algorithm.