There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The k-means method is a widely used clustering technique that seeks to minimize the average squared distance between points in the same cluster. Although it offers no accuracy guarantees, its simplicity and speed are very appealing in practice. By augmenting k-means with a very simple, randomized seeding technique, we obtain an algorithm that is Θ(logk)-competitive with the optimal clustering. Preliminary experiments show that our augmentation improves both the speed and the accuracy of k-means, often quite dramatically.

/pdf/k-means-the-advantages-of-careful-seeding-4p8vluc5ni.pdf

k-means++: the advantages of careful seeding

An integrated framework for sustainable supplier selection and evaluation in supply chains

Selecting green suppliers based on GSCM practices: Using Fuzzy TOPSIS applied to a Brazilian electronics company

Supply chain network design (SCND) models and methods have been the subject of several recent literature review surveys, but none of them explicitly includes sustainable development as a main characteristic of the problem considered. The aim of this review is to bridge this gap. The paper analyzes 87 papers in the field of supply chain network design, covering mathematical models that include economic factors as well as environmental and/or social dimensions. The review is organized along four research questions asking (i) which environmental and social objectives are included, (ii) how are they integrated into the models, (iii) which methods and tool are used and finally (iv) which industrial applications and contexts are covered in these models. The review finds that there are a number of limitations to the current research in sustainable SCND. The narrow scope of environmental and social measures in current models should go beyond limited greenhouse gas indicators to broader life-cycle approaches including new social metrics. The more effective inclusion of uncertainty and risk in models with improved multi-objective approaches is also needed. There are also significant gaps in the sectors used to test models limiting more general applicability. The paper concludes with promising new avenues of research to more effectively include sustainability into SCND models.

/pdf/sustainable-supply-chain-network-design-an-optimization-42wek3gyel.pdf

Sustainable supply chain network design: An optimization-oriented review☆

As the green movement spreads across the globe, organizations are under pressure to reduce the emissions across their supply chain. On the other hand, they need to cut supply costs to gain a competitive edge. This paper proposes Green DEA (GDEA), a comprehensive approach based on Data Envelopment Analysis (DEA) with carbon footprint monitoring. GDEA builds on an existing DEA model with weight restrictions and dual role factors, and introduces carbon footprints as necessary dual role factors with weight restrictions. Unlike other researches, GDEA incorporates heterogeneous suppliers and also takes into account regional emission compliance standards and laws. GDEA encourages suppliers to go green and cut down their carbon footprints and comply with emission norms along with reducing costs in order to survive competition. Results from model validation in a well-known automobile spare parts manufacturer in India are presented to verify the GDEA approach. Overall, GDEA cuts across a huge and varied supplier base, caters to almost all businesses, is environment-friendly and robust.

A comprehensive environment friendly approach for supplier selection

This paper presents an electronic travel aid for blind people to navigate safely and quickly, an obstacle detection system using ultrasonic sensors and USB camera based visual navigation has been considered. The proposed system detects the obstacles up to 300 cm via sonar and sends feedback (beep sound) to inform the person about its location. In addition to this, an USB webcam is connected with eBox 2300™ Embedded System for capturing the field of view of the user, which is used for finding the properties of the obstacle in particular, in the context of this work, locating a human being. Identification of human presence is based on face detection and cloth texture analysis. The major constraints for these algorithms to run on Embedded System are small image frame (160×120) having reduced faces, limited memory and very less processing time available to achieve real time image processing requirements. The algorithms are implemented in C++ using Visual Studio 5.0 IDE, which runs on Windows CE™ environment.

An electronic travel aid for navigation of visually impaired persons

We consider the online problem of scheduling jobs on unrelated machines so as to minimize the total weighted flow time. This problem has an unbounded competitive ratio even for very restricted settings. In this paper we show that if we allow the machines of the online algorithm to have e more speed than those of the offline algorithm then we can get an O((1+e-1)2)-competitive algorithm. Our algorithm schedules jobs preemptively but without migration. However, we compare our solution to an offline algorithm which allows migration. Our analysis uses a potential function argument which can also be extended to give a simpler and better proof of the randomized immediate dispatch algorithm of Chekuri-Goel-Khanna-Kumar for minimizing average flow time on parallel machines.

https://www.cse.iitd.ac.in/~amitk/262-chadha.pdf

A competitive algorithm for minimizing weighted flow time on unrelatedmachines with speed augmentation

We present the first linear time (1+e)-approximation algorithm for the k-means problem for fixed k and e. Our algorithm runs in O(nd) time, which is linear in the size of the input. Another feature of our algorithm is its simplicity - the only technique involved is random sampling.

Amit Kumar

Papers

A comprehensive environment friendly approach for supplier selection

An electronic travel aid for navigation of visually impaired persons

A competitive algorithm for minimizing weighted flow time on unrelatedmachines with speed augmentation

A simple linear time ( 1+ ε)- approximation algorithm for geometric k-means clustering in any dimensions

Development of PEGDMA: MAA based hydrogel microparticles for oral insulin delivery.