Asymptotically optimal declustering schemes for 2-dim range queries

AbstractDeclustering techniques have been widely adopted in parallel storage systems (e.g. disk arrays) to speed up bulk retrieval of multidimensional data. A declustering scheme distributes data items among multiple disks, thus enabling parallel data access and reducing query response time. We measure the performance of any declustering scheme as its worst case additive deviation from the ideal scheme. The goal thus is to design declustering schemes with as small an additive error as possible. We describe a number of declustering schemes with additive error O(logM) for 2-dimensional range queries, where M is the number of disks. These are the first results giving O(logM) upper bound for all values of M. Our second result is a lower bound on the additive error. It is known that except for a few stringent cases, additive error of any 2-dimensional declustering scheme is at least one. We strengthen this lower bound to Ω((logM)(d−1/2)) for d-dimensional schemes and to Ω(logM) for 2-dimensional schemes, thus proving that the 2-dimensional schemes described in this paper are (asymptotically) optimal. These results are obtained by establishing a connection to geometric discrepancy. We also present simulation results to evaluate the performance of these schemes in practice

The Loading Time Scheduling Problem

In this paper we study precedence constrained scheduling problems, where the tasks can only be executed on a specified subset of the machines. Each machine has a loading time that is incurred only for the first task that is scheduled on the machine in a particular run. This basic scheduling problem arises in the context of machining on numerically controlled machines, query optimization in databases, and in other artificial intelligence applications. We give the first non-trivial approximation algorithm for this problem. We also prove non-trivial lower bounds on best possible approximation ratios for these problems. These improve on the non-approximability results that are implied by the non-approximability results for the shortests common supersequence problem. We use the same algorithmic technique to obtain approximation algorithms for a problem arising in the context of code generation for parallel machines, and for the weighted shortest common supersequence problem

Facility Location with Dynamic Distance Functions

Facility location problems have always been studied with the assumption that the edge lengths in the network are {\em static} and do not change over time. The underlying network could be used to model a city street network for emergency facility location/hospitals, or an electronic network for locating information centers. In any case, it is clear that due to traffic congestion the traversal time on links {\em changes} with time. Very often, we have some estimates as to how the edge lengths change over time, and our objective is to choose a set of locations (vertices) as centers, such that at {\em every} time instant each vertex has a center close to it (clearly, the center close to a vertex may change over time). We also provide approximation algorithms as well as hardness results for the $K$-center problem under this model. This is the first comprehensive study regarding approximation algorithms for facility location for good time-invariant solutions. (Also cross-references as UMIACS-TR-97-70

Nations within a nation: variations in epidemiological transition across the states of India, 1990–2016 in the Global Burden of Disease Study

18% of the world's population lives in India, and many states of India have populations similar to those of large countries. Action to effectively improve population health in India requires availability of reliable and comprehensive state-level estimates of disease burden and risk factors over time. Such comprehensive estimates have not been available so far for all major diseases and risk factors. Thus, we aimed to estimate the disease burden and risk factors in every state of India as part of the Global Burden of Disease (GBD) Study 2016

Research Summary

mmunication in the other direction. Typically, servers can and must send much more data to clients than clients send back to the servers. Examples include wireless networks with mobile clients, cable and satellite systems, push based technology used for broadcasting "heavily" used web pages etc. A common theme in all these applications is the use of broadcast as a means of information dispersal: the server has n pages which the clients need; the server can broadcast a fixed number of pages in each time slot; an arbitrary client wishing to access a particular page listens to the broadcast channel until its page appears on the channel. Given the access pattern (hit probabilities) of the n pages, an efficient broadcast schedule is one which minimizes the expected waiting time of the clients. We formulated a periodic scheduling problem [2] which models this broadcast application. Surprisingly

Characterizing achievable multicast rates in multi-hop wireless networks

In this paper, we consider the multicast throughput optimization problem in multi-hop wireless networks. Given a source, and a set of receivers, we would like to find the set of multicast trees and a schedule such that the rate that the source can multicast to the receivers is maximized. We consider two transmission models: broadcast and unicast. In the broadcast model, a transmission is received bymultiple downstream nodes in a multicast tree. In the unicast model, a separate transmission has to be sent to each downstream node. We consider the fundamental constraint that a node can not be involved in multiple communications at the same time. We consider two multicast models: a single multicast tree per session and multiple multicast tree per session. In the single multicast tree case, (1) for the unicast model, we show that the problem is NP-hard an

On Power Efficient Communication over Multi-hop Wireless Networks: Joint Routing, Scheduling and Power Control

With increasing interest in energy constrained multi-hop wireless networks [2], a fundamental problem is one of determining energy efficient communication strategies over these multi-hop networks. The simplest problem is one where a given source node wants to communicate with a given destination, with a given rate over a multi-hop wireless network, using minimum power. Here the power refers to the total amount of power consumed over the entire network in order to achieve this rate between the source and the destination. There are three decisions that have to be made (jointly) in order to minimize the power requirement. • The path(s) that..