VIEWPOINT: Hinduism and the Academy: Towards a Dialogue Between Scholar and Practitioner

Gupta articlulates a rationale as to why the position of both the academician and the practitioner are necessary for meaningful religious dialog

He is our master : Jesus in the Thought of Swami Prabhupada

Now that steam, electricity, and the printing press have brought into closer communication the different races that inhabit the earth, and have expanded the minds of men, tending to dispel the illusion that God Almighty especially favours any particular people, it is time to proclaim to the world, that if a messenger of God appeared in Judea about nineteen hundred years ago, it is no less true that a messenger from the same God appeared in the quiet town of Navadweep (popularly known as Nadia) in Bengal, some fifteen centuries later. The former is known by the name of Jesus Christ; the latter is known in India by the name of Sree Gauranga, Sree Krishna Chaitanya, and several other names. If wonders attended Jesus, so also they attended Sree Gauranga of Nadia. The Christians have conferred an inestimable obligation upon those Hindus whose faith has been affected by Western materialism, by presenting Christ to them; and they, as a grateful return, are anxious to present Sree Krishna and Sree Gauranga to the people of the West. So begins Shishir Kumar Ghose\u27s lengthy biography of Caitanya, published at the turn of the twentieth century

Approximation Algorithms for Optimal Decision Trees and Adaptive TSP Problems

We consider the problem of constructing optimal decision trees: given a collection of tests which can disambiguate between a set of $m$ possible diseases, each test having a cost, and the a-priori likelihood of the patient having any particular disease, what is a good adaptive strategy to perform these tests to minimize the expected cost to identify the disease? We settle the approximability of this problem by giving a tight $O(\log m)$-approximation algorithm. We also consider a more substantial generalization, the Adaptive TSP problem. Given an underlying metric space, a random subset $S$ of cities is drawn from a known distribution, but $S$ is initially unknown to us--we get information about whether any city is in $S$ only when we visit the city in question. What is a good adaptive way of visiting all the cities in the random subset $S$ while minimizing the expected distance traveled? For this problem, we give the first poly-logarithmic approximation, and show that this algorithm is best possible unless we can improve the approximation guarantees for the well-known group Steiner tree problem.Comment: 28 pages; to appear in Mathematics of Operations Researc

Robust and MaxMin Optimization under Matroid and Knapsack Uncertainty Sets

Consider the following problem: given a set system (U,I) and an edge-weighted graph G = (U, E) on the same universe U, find the set A in I such that the Steiner tree cost with terminals A is as large as possible: "which set in I is the most difficult to connect up?" This is an example of a max-min problem: find the set A in I such that the value of some minimization (covering) problem is as large as possible. In this paper, we show that for certain covering problems which admit good deterministic online algorithms, we can give good algorithms for max-min optimization when the set system I is given by a p-system or q-knapsacks or both. This result is similar to results for constrained maximization of submodular functions. Although many natural covering problems are not even approximately submodular, we show that one can use properties of the online algorithm as a surrogate for submodularity. Moreover, we give stronger connections between max-min optimization and two-stage robust optimization, and hence give improved algorithms for robust versions of various covering problems, for cases where the uncertainty sets are given by p-systems and q-knapsacks.Comment: 17 pages. Preliminary version combining this paper and http://arxiv.org/abs/0912.1045 appeared in ICALP 201

Approximation Algorithms for Correlated Knapsacks and Non-Martingale Bandits

In the stochastic knapsack problem, we are given a knapsack of size B, and a set of jobs whose sizes and rewards are drawn from a known probability distribution. However, we know the actual size and reward only when the job completes. How should we schedule jobs to maximize the expected total reward? We know O(1)-approximations when we assume that (i) rewards and sizes are independent random variables, and (ii) we cannot prematurely cancel jobs. What can we say when either or both of these assumptions are changed? The stochastic knapsack problem is of interest in its own right, but techniques developed for it are applicable to other stochastic packing problems. Indeed, ideas for this problem have been useful for budgeted learning problems, where one is given several arms which evolve in a specified stochastic fashion with each pull, and the goal is to pull the arms a total of B times to maximize the reward obtained. Much recent work on this problem focus on the case when the evolution of the arms follows a martingale, i.e., when the expected reward from the future is the same as the reward at the current state. What can we say when the rewards do not form a martingale? In this paper, we give constant-factor approximation algorithms for the stochastic knapsack problem with correlations and/or cancellations, and also for budgeted learning problems where the martingale condition is not satisfied. Indeed, we can show that previously proposed LP relaxations have large integrality gaps. We propose new time-indexed LP relaxations, and convert the fractional solutions into distributions over strategies, and then use the LP values and the time ordering information from these strategies to devise a randomized adaptive scheduling algorithm. We hope our LP formulation and decomposition methods may provide a new way to address other correlated bandit problems with more general contexts

Dial a Ride from k-forest

The k-forest problem is a common generalization of both the k-MST and the dense-$k$-subgraph problems. Formally, given a metric space on $n$ vertices $V$, with $m$ demand pairs $\subseteq V \times V$ and a ``target'' $k\le m$, the goal is to find a minimum cost subgraph that connects at least $k$ demand pairs. In this paper, we give an $O(\min\{\sqrt{n},\sqrt{k}\})$-approximation algorithm for $k$-forest, improving on the previous best ratio of $O(n^{2/3}\log n)$ by Segev & Segev. We then apply our algorithm for k-forest to obtain approximation algorithms for several Dial-a-Ride problems. The basic Dial-a-Ride problem is the following: given an $n$ point metric space with $m$ objects each with its own source and destination, and a vehicle capable of carrying at most $k$ objects at any time, find the minimum length tour that uses this vehicle to move each object from its source to destination. We prove that an $\alpha$-approximation algorithm for the $k$-forest problem implies an $O(\alpha\cdot\log^2n)$-approximation algorithm for Dial-a-Ride. Using our results for $k$-forest, we get an $O(\min\{\sqrt{n},\sqrt{k}\}\cdot\log^2 n)$- approximation algorithm for Dial-a-Ride. The only previous result known for Dial-a-Ride was an $O(\sqrt{k}\log n)$-approximation by Charikar & Raghavachari; our results give a different proof of a similar approximation guarantee--in fact, when the vehicle capacity $k$ is large, we give a slight improvement on their results.Comment: Preliminary version in Proc. European Symposium on Algorithms, 200

Feature-based Approach for Semantic Interoperability of Shape Models

Semantic interoperability (SI) of a product model refers to automatic exchange of meaning associated with the product data, among applications/domains throughout the product development cycle. In the product development cycle, several applications (engineering design, industrial design, manufacturing, supply chain, marketing, maintenance etc.) and different engineering domains (mechanical, electrical, electronic etc.) come into play making the ability to exchange product data with semantics very significant. With product development happening in multiple locations with multiple tools/systems, SI between these systems/domains becomes important. The thesis presents a feature-based framework for shape model to address these SI issues when exchanging shape models. Problem of exchanging semantics associated with shape model to support the product lifecycle has been identified and explained. Different types of semantic interoperability issues pertaining to the shape model have been identified and classified. Features in a shape model can be associated with volume addition/subtraction to/from base-solid, deformation/modification of base-sheet/base surface, forming of material of constant thickness. The DIFF model has been extended to represent, classify and extract Free-Form Surface Features (FFSFs) and deformation features in a part model. FFSFs refer to features that modify a free-form surface. Deformation features are created in constant thickness part models, for example, deformation of material (as in sheet-metal parts) or forming of material (as in injection molded parts with constant thickness), also referred to as constant thickness features. Volumetric features covered in the DIFF model have been extended to classify and represent volumetric features based on relative variations of cross-section and PathCurve. Shape feature ontology is described based on unified feature taxonomy with definitions and labels of features as defined in the extended DIFF model. Features definitions are used as intermediate and unambiguous representation for shape features. The feature ontology is used to capture semantics of shape features. The proposed ontology enables reasoning to handle semantic equivalences between feature labels, and is used to map shape features from a source to target applications. Reasoning framework for identification of semantically equivalent feature labels and representations for the feature being exchanged across multiple applications is presented and discussed. This reasoning framework is used to associate multiple construction paths for a feature and associate applicable meanings from the ontology. Interface is provided to select feature label for a target application from the list of labels which are semantically equivalent for the feature being exchanged/mapped. Parameters for the selected feature label can be mapped from the DIFF representation; the feature can then be represented/constructed in the target application using the feature label and mapped parameters. This work shows that product model with feature information (feature labels and representations), as understood by the target application, can be exchanged and maintained in such a way that multiple applications can use the product information as their understandable labels and representations. Finally, the thesis concludes by summarizing the main contributions and outlining the scope for future work