Distributed Maximum Matching in Bounded Degree Graphs

We present deterministic distributed algorithms for computing approximate maximum cardinality matchings and approximate maximum weight matchings. Our algorithm for the unweighted case computes a matching whose size is at least (1-\eps) times the optimal in \Delta^{O(1/\eps)} + O\left(\frac{1}{\eps^2}\right) \cdot\log^*(n) rounds where $n$ is the number of vertices in the graph and $\Delta$ is the maximum degree. Our algorithm for the edge-weighted case computes a matching whose weight is at least (1-\eps) times the optimal in \log(\min\{1/\wmin,n/\eps\})^{O(1/\eps)}\cdot(\Delta^{O(1/\eps)}+\log^*(n)) rounds for edge-weights in [\wmin,1]. The best previous algorithms for both the unweighted case and the weighted case are by Lotker, Patt-Shamir, and Pettie~(SPAA 2008). For the unweighted case they give a randomized (1-\eps)-approximation algorithm that runs in O((\log(n)) /\eps^3) rounds. For the weighted case they give a randomized (1/2-\eps)-approximation algorithm that runs in O(\log(\eps^{-1}) \cdot \log(n)) rounds. Hence, our results improve on the previous ones when the parameters $\Delta$, \eps and \wmin are constants (where we reduce the number of runs from $O(\log(n))$ to $O(\log^*(n))$), and more generally when $\Delta$, 1/\eps and 1/\wmin are sufficiently slowly increasing functions of $n$. Moreover, our algorithms are deterministic rather than randomized.Comment: arXiv admin note: substantial text overlap with arXiv:1402.379

Best of Two Local Models: Local Centralized and Local Distributed Algorithms

We consider two models of computation: centralized local algorithms and local distributed algorithms. Algorithms in one model are adapted to the other model to obtain improved algorithms. Distributed vertex coloring is employed to design improved centralized local algorithms for: maximal independent set, maximal matching, and an approximation scheme for maximum (weighted) matching over bounded degree graphs. The improvement is threefold: the algorithms are deterministic, stateless, and the number of probes grows polynomially in $\log^* n$, where $n$ is the number of vertices of the input graph. The recursive centralized local improvement technique by Nguyen and Onak~\cite{onak2008} is employed to obtain an improved distributed approximation scheme for maximum (weighted) matching. The improvement is twofold: we reduce the number of rounds from $O(\log n)$ to $O(\log^*n)$ for a wide range of instances and, our algorithms are deterministic rather than randomized

Nuclear Density Dependence of In-Medium Polarization

It is shown that polarization transfer measurements $(\vec{e},e'\vec{p})$ on a specific target nucleus can provide constraints on the ratio of the in-medium electric to magnetic form factor. Thereby one exploits the fact that proton knockout from single-particle levels exhibit a specific sensitivity to the effective nuclear density. It is shown that in $^{12}$C the effective nuclear density for $s$-shell knockout is about twice as high as for $p$-shell knockout. With current model predictions for the in-medium form factors, one obtains measurable modifications of the order of 5% in the ratios of the double polarization observables between those single-particle levels

A Deep Moving-camera Background Model

In video analysis, background models have many applications such as background/foreground separation, change detection, anomaly detection, tracking, and more. However, while learning such a model in a video captured by a static camera is a fairly-solved task, in the case of a Moving-camera Background Model (MCBM), the success has been far more modest due to algorithmic and scalability challenges that arise due to the camera motion. Thus, existing MCBMs are limited in their scope and their supported camera-motion types. These hurdles also impeded the employment, in this unsupervised task, of end-to-end solutions based on deep learning (DL). Moreover, existing MCBMs usually model the background either on the domain of a typically-large panoramic image or in an online fashion. Unfortunately, the former creates several problems, including poor scalability, while the latter prevents the recognition and leveraging of cases where the camera revisits previously-seen parts of the scene. This paper proposes a new method, called DeepMCBM, that eliminates all the aforementioned issues and achieves state-of-the-art results. Concretely, first we identify the difficulties associated with joint alignment of video frames in general and in a DL setting in particular. Next, we propose a new strategy for joint alignment that lets us use a spatial transformer net with neither a regularization nor any form of specialized (and non-differentiable) initialization. Coupled with an autoencoder conditioned on unwarped robust central moments (obtained from the joint alignment), this yields an end-to-end regularization-free MCBM that supports a broad range of camera motions and scales gracefully. We demonstrate DeepMCBM's utility on a variety of videos, including ones beyond the scope of other methods. Our code is available at https://github.com/BGU-CS-VIL/DeepMCBM .Comment: 26 paged, 5 figures. To be published in ECCV 202