Randomized Composable Core-sets for Distributed Submodular Maximization

An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution inside the union of the representative solutions for all pieces. This technique can be captured via the concept of {\em composable core-sets}, and has been recently applied to solve diversity maximization problems as well as several clustering problems. However, for coverage and submodular maximization problems, impossibility bounds are known for this technique \cite{IMMM14}. In this paper, we focus on efficient construction of a randomized variant of composable core-sets where the above idea is applied on a {\em random clustering} of the data. We employ this technique for the coverage, monotone and non-monotone submodular maximization problems. Our results significantly improve upon the hardness results for non-randomized core-sets, and imply improved results for submodular maximization in a distributed and streaming settings. In summary, we show that a simple greedy algorithm results in a $1/3$-approximate randomized composable core-set for submodular maximization under a cardinality constraint. This is in contrast to a known $O({\log k\over \sqrt{k}})$ impossibility result for (non-randomized) composable core-set. Our result also extends to non-monotone submodular functions, and leads to the first 2-round MapReduce-based constant-factor approximation algorithm with $O(n)$ total communication complexity for either monotone or non-monotone functions. Finally, using an improved analysis technique and a new algorithm $\mathsf{PseudoGreedy}$, we present an improved $0.545$-approximation algorithm for monotone submodular maximization, which is in turn the first MapReduce-based algorithm beating factor $1/2$ in a constant number of rounds

Venous tumor thrombus from a pelvic osteosarcoma

AbstractWe present a case of pelvic osteosarcoma in an 18-year-old woman with a tumor thrombus in the left iliac vein, extending to the inferior vena cava. Tumor thrombus has been rarely described with osteosarcoma, with only 14 cases in the literature

Advances on Matroid Secretary Problems: Free Order Model and Laminar Case

The most well-known conjecture in the context of matroid secretary problems claims the existence of a constant-factor approximation applicable to any matroid. Whereas this conjecture remains open, modified forms of it were shown to be true, when assuming that the assignment of weights to the secretaries is not adversarial but uniformly random (Soto [SODA 2011], Oveis Gharan and Vondr\'ak [ESA 2011]). However, so far, there was no variant of the matroid secretary problem with adversarial weight assignment for which a constant-factor approximation was found. We address this point by presenting a 9-approximation for the \emph{free order model}, a model suggested shortly after the introduction of the matroid secretary problem, and for which no constant-factor approximation was known so far. The free order model is a relaxed version of the original matroid secretary problem, with the only difference that one can choose the order in which secretaries are interviewed. Furthermore, we consider the classical matroid secretary problem for the special case of laminar matroids. Only recently, a constant-factor approximation has been found for this case, using a clever but rather involved method and analysis (Im and Wang, [SODA 2011]) that leads to a 16000/3-approximation. This is arguably the most involved special case of the matroid secretary problem for which a constant-factor approximation is known. We present a considerably simpler and stronger $3\sqrt{3}e\approx 14.12$-approximation, based on reducing the problem to a matroid secretary problem on a partition matroid

Estimation of surface turbulent heat fluxes via variational assimilation of sequences of land surface temperatures from Geostationary Operational Environmental Satellites

Recently, a number of studies have focused on estimating surface turbulent heat fluxes via assimilation of sequences of land surface temperature (LST) observations into variational data assimilation (VDA) schemes. Using the full heat diffusion equation as a constraint, the surface energy balance equation can be solved via assimilation of sequences of LST within a VDA framework. However, the VDA methods have been tested only in limited field sites that span only a few climate and land use types. Hence, in this study, combined-source (CS) and dual-source (DS) VDA schemes are tested extensively over six FluxNet sites with different vegetation covers (grassland, cropland, and forest) and climate conditions. The CS model groups the soil and canopy together as a single source and does not consider their different contributions to the total turbulent heat fluxes, while the DS model considers them to be different sources. LST data retrieved from the Geostationary Operational Environmental Satellites are assimilated into these two VDA schemes. Sensible and latent heat flux estimates from the CS and DS models are compared with the corresponding measurements from flux tower stations. The results indicate that the performance of both models at dry, lightly vegetated sites is better than that at wet, densely vegetated sites. Additionally, the DS model outperforms the CS model at all sites, implying that the DS scheme is more reliable and can characterize the underlying physics of the problem better

A PTAS for planar group Steiner tree via spanner bootstrapping and prize collecting

We present the first polynomial-time approximation scheme (PTAS), i.e., (1 + ϵ)-approximation algorithm for any constant ϵ > 0, for the planar group Steiner tree problem (in which each group lies on a boundary of a face). This result improves on the best previous approximation factor of O(logn(loglogn)O(1)). We achieve this result via a novel and powerful technique called spanner bootstrapping, which allows one to bootstrap from a superconstant approximation factor (even superpolynomial in the input size) all the way down to a PTAS. This is in contrast with the popular existing approach for planar PTASs of constructing lightweight spanners in one iteration, which notably requires a constant-factor approximate solution to start from. Spanner bootstrapping removes one of the main barriers for designing PTASs for problems which have no known constant-factor approximation (even on planar graphs), and thus can be used to obtain PTASs for several difficult-to-approximate problems. Our second major contribution required for the planar group Steiner tree PTAS is a spanner construction, which reduces the graph to have total weight within a factor of the optimal solution while approximately preserving the optimal solution. This is particularly challenging because group Steiner tree requires deciding which terminal in each group to connect by the tree, making it much harder than recent previous approaches to construct spanners for planar TSP by Klein [SIAM J. Computing 2008], subset TSP by Klein [STOC 2006], Steiner tree by Borradaile, Klein, and Mathieu [ACM Trans. Algorithms 2009], and Steiner forest by Bateni, Hajiaghayi, and Marx [J. ACM 2011] (and its improvement to an efficient PTAS by Eisenstat, Klein, and Mathieu [SODA 2012]. The main conceptual contribution here is realizing that selecting which terminals may be relevant is essentially a complicated prize-collecting process: we have to carefully weigh the cost and benefits of reaching or avoiding certain terminals in the spanner. Via a sequence of involved prize-collecting procedures, we can construct a spanner that reaches a set of terminals that is sufficient for an almost-optimal solution. Our PTAS for planar group Steiner tree implies the first PTAS for geometric Euclidean group Steiner tree with obstacles, as well as a (2 + ϵ)-approximation algorithm for group TSP with obstacles, improving over the best previous constant-factor approximation algorithms. By contrast, we show that planar group Steiner forest, a slight generalization of planar group Steiner tree, is APX-hard on planar graphs of treewidth 3, even if the groups are pairwise disjoint and every group is a vertex or an edge

The long term effects of occupational electromagnetic fields exposure on peripheral blood indexes in workers of aluminum processing factory of Arak

زمینه و هدف: نظریه بیماری زا بودن میدان های الکترومغناطیسی بر روی ساکنان و کارکنان مجاور این میدان ها بخصوص کارسینوژن بودن آنها مورد مطالعات زیادی قرار گرفته است. ولی نتایج آنها قطعیت نیافته و هنوز مناقشات زیادی در این مورد وجود دارد. این تحقیق به منظور بررسی اثر میدان های الکترومغناطیسی با شدت بالا بر شاخص های خون محیطی افرادی که بطور طولانی مدت (حداقل سه سال) در مجاورت این میدان ها بوده اند طراحی و اجرا گردید. روش بررسی: در یک مطالعه آینده نگر کارگرانی که در کارگاه الکترولیز کارخانه آلومینیوم اراک کار می کنند مورد بررسی قرار گرفتند. ابتدا با کمک گروه بهداشت صنعتی از قسمت های مختلف کارگاه الکترولیز گوس متری به عمل آمد و سپس دویست نفر از کارگران شاغل در کارگاه انتخاب و دویست نفر نیز از افرادی که در سایر قسمت ها شاغل بوده و در معرض میدان مغناطیسی نبودند با رعایت معیارهای ورود انتخاب شدند و هر دو گروه از نظر شرح حال، معاینه بالینی بررسی و پرسشنامه برای آنها تکمیل شد. سپس در دو نوبت به فاصله یکسال برای هر دو گروه CBC و شمارش پلاکت انجام شد. نهایتاً داده ها با استفاده از آمار توصیفی و تحلیلی (t مستقل) و نرم افزار SPSS تجزیه و تحلیل گردید. یافته ها: افراد دو گروه از نظر میانگین سنی و جنسی تفاوتی نداشتند. میانگین شاخص های خونی گروه مواجهه یافته در دو سال متوالی در رده گلبول های سفید، نوتروفیل ها، گلبول های قرمز، هموگلوبین، هماتوکریت و MCV بیشتر از گروه مواجهه نیافته بود (05/0

Pricing Multi-Unit Markets

We study the power and limitations of posted prices in multi-unit markets, where agents arrive sequentially in an arbitrary order. We prove upper and lower bounds on the largest fraction of the optimal social welfare that can be guaranteed with posted prices, under a range of assumptions about the designer's information and agents' valuations. Our results provide insights about the relative power of uniform and non-uniform prices, the relative difficulty of different valuation classes, and the implications of different informational assumptions. Among other results, we prove constant-factor guarantees for agents with (symmetric) subadditive valuations, even in an incomplete-information setting and with uniform prices

Streaming Algorithms for Submodular Function Maximization

We consider the problem of maximizing a nonnegative submodular set function $f:2^{\mathcal{N}} \rightarrow \mathbb{R}^+$ subject to a $p$-matchoid constraint in the single-pass streaming setting. Previous work in this context has considered streaming algorithms for modular functions and monotone submodular functions. The main result is for submodular functions that are {\em non-monotone}. We describe deterministic and randomized algorithms that obtain a $\Omega(\frac{1}{p})$-approximation using $O(k \log k)$-space, where $k$ is an upper bound on the cardinality of the desired set. The model assumes value oracle access to $f$ and membership oracles for the matroids defining the $p$-matchoid constraint.Comment: 29 pages, 7 figures, extended abstract to appear in ICALP 201

KINEMATICS OF THE FOOT AND ANKLE IN FORWARD ICE HOCKEY SKATING

Three elite ice hockey players performed forward skating with twin axis electro-goniometers placed posterior to the right ankle and rear foot. The data were gathered at a sampling frequency of 200 Hz. The use of mini notebook computer and data acquisition card allowed for a completely portable system. Maximum and minimum range of motion data were averaged for inversion-eversion and dorsiflexion-plantarflexion motions were examined throughout one stride cycle

Partitioning SKA Dataflows for Optimal Graph Execution

Optimizing data-intensive workflow execution is essential to many modern scientific projects such as the Square Kilometre Array (SKA), which will be the largest radio telescope in the world, collecting terabytes of data per second for the next few decades. At the core of the SKA Science Data Processor is the graph execution engine, scheduling tens of thousands of algorithmic components to ingest and transform millions of parallel data chunks in order to solve a series of large-scale inverse problems within the power budget. To tackle this challenge, we have developed the Data Activated Liu Graph Engine (DALiuGE) to manage data processing pipelines for several SKA pathfinder projects. In this paper, we discuss the DALiuGE graph scheduling sub-system. By extending previous studies on graph scheduling and partitioning, we lay the foundation on which we can develop polynomial time optimization methods that minimize both workflow execution time and resource footprint while satisfying resource constraints imposed by individual algorithms. We show preliminary results obtained from three radio astronomy data pipelines.Comment: Accepted in HPDC ScienceCloud 2018 Worksho