1,034 research outputs found

    Approximation algorithms for Capacitated Facility Location Problem with Penalties

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    In this paper, we address the problem of capacitated facility location problem with penalties (CapFLPP) paid per unit of unserved demand. In case of uncapacitated FLP with penalties demands of a client are either entirely met or are entirely rejected and penalty is paid. In the uncapacitated case, there is no reason to serve a client partially. Whereas, in case of CapFLPP, it may be beneficial to serve a client partially instead of not serving at all and, pay the penalty for the unmet demand. Charikar et. al. \cite{charikar2001algorithms}, Jain et. al. \cite{jain2003greedy} and Xu- Xu \cite{xu2009improved} gave 33, 22 and 1.85261.8526 approximation, respectively, for the uncapacitated case . We present (5.83+ϵ)(5.83 + \epsilon) factor for the case of uniform capacities and (8.532+ϵ)(8.532 + \epsilon) factor for non-uniform capacities

    Discrete functional inequalities on lattice graphs

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    In this thesis, we study problems at the interface of analysis and discrete mathematics. We discuss analogues of well known Hardy-type inequalities and Rearrangement inequalities on the lattice graphs Z^d, with a particular focus on behaviour of sharp constants and optimizers. In the first half of the thesis, we analyse Hardy inequalities on Z^d, first for d=1 and then for d >= 3. We prove a sharp weighted Hardy inequality on integers with power weights of the form n^\alpha. This is done via two different methods, namely 'super-solution' and 'Fourier method'. We also use Fourier method to prove a weighted Hardy type inequality for higher order operators. After discussing the one dimensional case, we study the Hardy inequality in higher dimensions (d >= 3). In particular, we compute the asymptotic behaviour of the sharp constant in the discrete Hardy inequality, as d \rightarrow \infty. This is done by converting the inequality into a continuous Hardy-type inequality on a torus for functions having zero average. These continuous inequalities are new and interesting in themselves. In the second half, we focus our attention on analogues of Rearrangement inequalities on lattice graphs. We begin by analysing the situation in dimension one. We define various notions of rearrangements and prove the corresponding Polya-Szego inequality. These inequalities are also applied to prove some weighted Hardy inequalities on integers. Finally, we study Rearrangement inequalities (Polya-Szego) on general graphs, with a particular focus on lattice graphs Z^d, for d >=2. We develop a framework to study these inequalities, using which we derive concrete results in dimension two. In particular, these results develop connections between Polya-Szego inequality and various isoperimetric inequalities on graphs.Open Acces

    Generalizing Deep Learning Methods for Particle Tracing Using Transfer Learning

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    Particle tracing is a very important method for scientific visualization of vector fields, but it is computationally expensive. Deep learning can be used to speed up particle tracing, but existing deep learning models are domain-specific. In this work, we present a methodology to generalize the use of deep learning for particle tracing using transfer learning. We demonstrate the performance of our approach through a series of experimental studies that address the most common simulation design scenarios: varying time span, Reynolds number, and problem geometry. The results show that our methodology can be effectively used to generalize and accelerate the training and practical use of deep learning models for visualization of unsteady flows

    Articulation-aware Canonical Surface Mapping

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    We tackle the tasks of: 1) predicting a Canonical Surface Mapping (CSM) that indicates the mapping from 2D pixels to corresponding points on a canonical template shape, and 2) inferring the articulation and pose of the template corresponding to the input image. While previous approaches rely on keypoint supervision for learning, we present an approach that can learn without such annotations. Our key insight is that these tasks are geometrically related, and we can obtain supervisory signal via enforcing consistency among the predictions. We present results across a diverse set of animal object categories, showing that our method can learn articulation and CSM prediction from image collections using only foreground mask labels for training. We empirically show that allowing articulation helps learn more accurate CSM prediction, and that enforcing the consistency with predicted CSM is similarly critical for learning meaningful articulation.Comment: To appear at CVPR 2020, project page https://nileshkulkarni.github.io/acsm

    Inter Process Communication and Prioritization to Enable Desktop Advertisement Mechanism

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    This research paper tries to bring in a new concept of desktop advertising mechanism by synchronization it with the running processes and the data on users’ side. The proposed approach shall be based on inter process communication interaction, scheduling, prioritization, desktop crawling and system calls. The running process status and data will be fetched by the proposed process, which will then seek relevant information with the remote ad server and display the advertisements fetched based on keywords on user side