Abstract. We consider fundamental scheduling problems motivated by energy issues. In this framework, we are given a set of jobs, each with a release time, deadline and required processing length. The jobs need to be scheduled on a machine so that at most g jobs are active at any given time. The duration for which a machine is active (i.e., "on") is referred to as its active time. The goal is to find a feasible schedule for all jobs, minimizing the total active time. When preemption is allowed at integer time points, we show that a minimal feasible schedule already yields a 3-approximation (and this bound is tight) and we further improve this to a 2-approximation via LP rounding techniques. Our second contribution is for the non-preemptive version of this problem. However, since even asking if a feasible schedule on one machine exists is NP-hard, we allow for an unbounded number of virtual machines, each having capacity of g. This problem is known as the busy time problem in the literature and a 4-approximation is known for this problem. We develop a new combinatorial algorithm that gives a 3-approximation. Furthermore, we consider the preemptive busy time problem, giving a simple and exact greedy algorithm when unbounded parallelism is allowed, i.e., g is unbounded. For arbitrary g, this yields an algorithm that is 2-approximate.

Abstract-Frequently, ISPs charge for Internet use not based on peak bandwidth usage, but according to a percentile (often the 95th percentile) cost model. In other words, the time slots with the top 5 percent (in the case of 95th percentile) of data transmission volume do not affect the cost of transmission. Instead, we are charged based on the volume of traffic sent in the 95th percentile slot. In such an environment, by allowing a short delay in transmission of some data, we may be able to reduce our cost considerably.We provide an optimal solution to the offline version of this problem (in which the job arrivals are known), for any delay D > 0. The algorithm works for any choice of percentile. We also show that there is no efficient deterministic online algorithm for this problem. However, for a slightly different problem, where the maximum amount of data transmitted is used for cost accounting, we provide an online algorithm with a competitive ratio of 2D+1 D+1. Furthermore, we prove that no online algorithm can achieve a competitive ratio better thanwherei D+i for any D > 0 in an adversarial setting.We also provide a heuristic that can be used in an online setting where the network traffic has a strong correlation over consecutive accounting cycles, based on the solution to the offline percentile problem. Experimental results are used to illustrate the performance of the algorithms proposed in this work.

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Introduction:Jatyadi ghrita is a classical Ayurvedic formulation indicated in the treatment of various types of ulcers.Aim:The study was designed to explore the wound healing properties of Jatyadi Ghrita in diabetes - induced rats.Materials and Methods:In the present study, diabetes mellitus was induced to 6 to 8-week-old male Wistar rats by injecting streptozotocin cut 65 mg/kg body weight intravenously by 15 min prior to the administration of Nicotinamide at 230 mg/kg body weight intraperitoneally. Animals having diabetes were used for grouping namely, diabetic control (DC), Ghrita control (GC), positive control (PC), i.e., mupirocin HCl, Jatyadi Ghrita treatment and one group of non-DC. Full-thickness excision wound was created and diameter was recorded. Daily clinical observations were recorded. A wound scoring method was developed. Wound diameter and score were recorded on days 1, 2, 3, 5, 7, 9, 12, 14 and 15. Photographs were taken at the same time interval points. Body weight and feed consumption were recorded weekly. Animals were sacrificed at regular intervals to collect the wound area tissue for histopathology analysis. Obtained data was analyzed statistically.Results and Observation:It was observed that there was no significant difference in diameter and percent change in wound healing as compared to any control. However, clinical score and histopathological changes in Jatyadi Ghrita group were improved from the second day of the study as compared to control.Conclusion:This indicates that the drug has similar wound healing activity as compared to the modern drug mupirocin HCl.

Abstract-The energy costs for cooling a data center constitute a significant portion of the overall running costs. Thermal imbalance and hot spots that arise due to imbalanced workloads lead to significant wasted cooling effort -in order to ensure that no equipment is operating above a certain temperature, the data center may be cooled more than necessary. Therefore it is desirable to schedule the workload in a data center in a thermally aware manner, assigning jobs to machines not just based on local load of the machines, but based on the overall thermal profile of the data center. This is challenging because of the spatial cross-interference between machines, where a job assigned to a machine may impact not only that machine's temperature, but also nearby machines.Here, we continue formal analysis of the thermal scheduling problem that we initiated recently [25]. In that work, the notion of effective load of a machine which is a function of the local load on the machine as well as the load on nearby machines, was introduced, and optimal scheduling policies for a simple model (where cross-effects are restricted within a rack) were presented, under the assumption that jobs can be split among different machines. Here we consider the more realistic problem of integral assignment of jobs, and allow for cross-interference among different machines in adjacent racks in the data center. The integral assignment problem with cross-interference is NP-hard, even for a simple two machine model. We consider three different heat flow models, and give constant factor approximation algorithms for maximizing the number (or total profit) of jobs assigned in each model, without violating thermal constraints. We also consider the problem of minimizing the maximum temperature on any machine when all jobs need to be assigned, and give constant factor algorithms for this problem.