Approximation algorithms for Capacitated Facility Location Problem with Penalties

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 $3$, $2$ and $1.8526$ approximation, respectively, for the uncapacitated case . We present $(5.83 + \epsilon)$ factor for the case of uniform capacities and $(8.532 + \epsilon)$ factor for non-uniform capacities

Articulation-aware Canonical Surface Mapping

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

Multistage Air Traffic Flow Management under Capacity Uncertainty: A Robust and Adaptive Optimization Approach

In this paper, we study the first application of robust and adaptive optimization in the Air Traffic Flow Management (ATFM) problem. The existing models for network-wide ATFM assume deterministic capacity estimates across airports and sectors without taking into account the uncertainty in capacities induced by weather. We introduce a weather-front based approach to model the uncertainty inherent in airspace capacity estimates resulting from the impact of a small number of weather fronts moving across the National Airspace (NAS). The key advantage of our uncertainty set construction is the low-dimensionality (uncertainty in only two parameters govern the overall uncertainty set for each airspace element). We formulate the consequent ATFM problem under capacity uncertainty within the robust and adaptive optimization framework and propose tractable solution methodologies. Our theoretical contributions are as follows: i) we propose a polyhedral description of the convex hull of the discrete uncertainty set; ii) we prove the equivalence of the robust problem to a modified instance of the deterministic problem; and iii) we solve optimally the LP relaxation of the adaptive problem using piece-wise affine policies where the number of pieces in an optimal policy are governed by the number of extreme points in the uncertainty set. A particularly attractive feature is that for most practically encountered instances, an affine policy suffices to solve the adaptive problem optimally. Finally, we report empirical results from the proposed models on real world flight schedules augmented with simulated weather fronts that illuminate the merits of our proposal. The key insights from our computational results are: i) the robust problem inherits all the attractive properties of the deterministic problem (e.g., superior integrality properties and fast computational times); and ii) the price of robustness and adaptability is typically small.National Science Foundation (U.S.) (NSF Grant EFRI-0735905

Factoring Shape, Pose, and Layout from the 2D Image of a 3D Scene

The goal of this paper is to take a single 2D image of a scene and recover the 3D structure in terms of a small set of factors: a layout representing the enclosing surfaces as well as a set of objects represented in terms of shape and pose. We propose a convolutional neural network-based approach to predict this representation and benchmark it on a large dataset of indoor scenes. Our experiments evaluate a number of practical design questions, demonstrate that we can infer this representation, and quantitatively and qualitatively demonstrate its merits compared to alternate representations.Comment: Project url with code: https://shubhtuls.github.io/factored3

Weak value amplification using asymmetric spectral response of Fano resonance as a natural pointer

Weak measurement enables faithful amplification and high precision measurement of small physical parameters and is under intensive investigation as an effective tool in metrology and for addressing foundational questions in quantum mechanics. Most of the experimental reports on weak measurements till date have employed external symmetric Gaussian pointers. Here, we demonstrate its universal nature in a system involving asymmetric spectral response of Fano resonance as the pointer arising naturally in precisely designed metamaterials, namely, waveguided plasmonic crystals. The weak coupling arises due to a tiny shift in the asymmetric spectral response between two orthogonal linear polarizations. By choosing the pre- and post-selected polarization states to be nearly mutually orthogonal, we observe both real and imaginary weak value amplifications manifested as spectacular shift of the peak frequency of Fano resonance and narrowing (or broadening) of the resonance line width, respectively. Weak value amplification using asymmetric Fano spectral response broadens the domain of applicability of weak measurements using natural spectral line shapes as pointer in wide range of physical systems