Constant Approximation for kk-Median and kk-Means with Outliers via Iterative Rounding

In this paper, we present a new iterative rounding framework for many clustering problems. Using this, we obtain an $(\alpha_1 + \epsilon \leq 7.081 + \epsilon)$-approximation algorithm for $k$-median with outliers, greatly improving upon the large implicit constant approximation ratio of Chen [Chen, SODA 2018]. For $k$-means with outliers, we give an $(\alpha_2+\epsilon \leq 53.002 + \epsilon)$-approximation, which is the first $O(1)$-approximation for this problem. The iterative algorithm framework is very versatile; we show how it can be used to give $\alpha_1$- and $(\alpha_1 + \epsilon)$-approximation algorithms for matroid and knapsack median problems respectively, improving upon the previous best approximations ratios of $8$ [Swamy, ACM Trans. Algorithms] and $17.46$ [Byrka et al, ESA 2015]. The natural LP relaxation for the $k$-median/$k$-means with outliers problem has an unbounded integrality gap. In spite of this negative result, our iterative rounding framework shows that we can round an LP solution to an almost-integral solution of small cost, in which we have at most two fractionally open facilities. Thus, the LP integrality gap arises due to the gap between almost-integral and fully-integral solutions. Then, using a pre-processing procedure, we show how to convert an almost-integral solution to a fully-integral solution losing only a constant-factor in the approximation ratio. By further using a sparsification technique, the additive factor loss incurred by the conversion can be reduced to any $\epsilon > 0$

Maximum gradient embeddings and monotone clustering

Let (X,d_X) be an n-point metric space. We show that there exists a distribution D over non-contractive embeddings into trees f:X-->T such that for every x in X, the expectation with respect to D of the maximum over y in X of the ratio d_T(f(x),f(y)) / d_X(x,y) is at most C (log n)^2, where C is a universal constant. Conversely we show that the above quadratic dependence on log n cannot be improved in general. Such embeddings, which we call maximum gradient embeddings, yield a framework for the design of approximation algorithms for a wide range of clustering problems with monotone costs, including fault-tolerant versions of k-median and facility location.Comment: 25 pages, 2 figures. Final version, minor revision of the previous one. To appear in "Combinatorica

Incremental Medians via Online Bidding

In the k-median problem we are given sets of facilities and customers, and distances between them. For a given set F of facilities, the cost of serving a customer u is the minimum distance between u and a facility in F. The goal is to find a set F of k facilities that minimizes the sum, over all customers, of their service costs. Following Mettu and Plaxton, we study the incremental medians problem, where k is not known in advance, and the algorithm produces a nested sequence of facility sets where the kth set has size k. The algorithm is c-cost-competitive if the cost of each set is at most c times the cost of the optimum set of size k. We give improved incremental algorithms for the metric version: an 8-cost-competitive deterministic algorithm, a 2e ~ 5.44-cost-competitive randomized algorithm, a (24+epsilon)-cost-competitive, poly-time deterministic algorithm, and a (6e+epsilon ~ .31)-cost-competitive, poly-time randomized algorithm. The algorithm is s-size-competitive if the cost of the kth set is at most the minimum cost of any set of size k, and has size at most s k. The optimal size-competitive ratios for this problem are 4 (deterministic) and e (randomized). We present the first poly-time O(log m)-size-approximation algorithm for the offline problem and first poly-time O(log m)-size-competitive algorithm for the incremental problem. Our proofs reduce incremental medians to the following online bidding problem: faced with an unknown threshold T, an algorithm submits "bids" until it submits a bid that is at least the threshold. It pays the sum of all its bids. We prove that folklore algorithms for online bidding are optimally competitive.Comment: conference version appeared in LATIN 2006 as "Oblivious Medians via Online Bidding

Multi-center, single-blind randomized controlled trial comparing functional electrical stimulation therapy to conventional therapy in incomplete tetraplegia

BackgroundLoss of upper extremity function after tetraplegia results in significant disability. Emerging evidence from pilot studies suggests that functional electrical stimulation (FES) therapy may enhance recovery of upper extremity function after tetraplegia. The aim of this trial was to determine the effectiveness of FES therapy delivered by the Myndmove stimulator in people with tetraplegia.MethodsA multi-center, single-blind, parallel-group, two-arm, randomized controlled trial was conducted comparing FES to conventional therapy in adults (≥18 years) with C4–C7 traumatic incomplete tetraplegia between 4 and 96 months post-injury, and with a baseline spinal cord injury independence measure III -self-care (SCIM III-SC) score of ≤10. Participants were enrolled at four SCI-specialized neurorehabilitation centers in the U.S. and Canada. Participants were stratified by center and randomized in a 1:1 ratio to receive either 40 sessions of FES or conventional therapy targeting upper extremities over a 14-week period. Blinded assessors measured SCIM III, Toronto Rehabilitation Institute Hand Function Test, and Graded Redefined Assessment of Strength, Sensibility, and Prehension at baseline, after 20th session, after 40th session or 14 weeks after 1st session, and at 24 weeks after 1st session. The primary outcome measure was change in SCIM III-SC from baseline to end of the treatment. Based on the primary outcome measure, a sample size of 60 was calculated. Seventeen participants' progress in the study was interrupted due to the COVID-19 lockdown. The protocol was modified for these participants to allow them to complete the study.ResultsBetween June 2019 to August 2021, 51 participants were randomized to FES (n = 27) and conventional therapy (n = 24). Both groups gained a mean of 2 points in SCIM-SC scores at the end of treatment, which was a clinically meaningful change. However, there was no statistically significant difference between the groups on any outcomes.ConclusionForty sessions of FES therapy delivered by the MyndMove stimulator are as effective as conventional therapy in producing meaningful functional improvements that persist after therapy is completed. Limitations of this study include the impact of COVID-19 limiting the ability to recruit the target sample size and per-protocol execution of the study in one-third of the participants.RegistrationThis trial is registered at www.ClinicalTrials.gov, NCT03439319

Magnetic Nano Cobalt Ferrite Catalyzed Synthesis of 4H-Pyrano[3,2-h]quinoline Derivatives under Microwave Irradiation

Abstract A microwave irradiated magnetically separable nano cobalt ferrite catalyzed green method for the synthesis of 4-phenyl-4H-pyrano[3,2-h]quinolin-2-amine and 2-amino-4-phenyl-4H-pyrano[3,2-h] quinoline-3-carbonitrile derivatives through cyclization of aromatic aldehyde, acetonitrile/malononitrile and 8-hydoxyquinoline is developed and presented in this paper. The cubic magnetic cobalt ferrite nano particles were synthesized by sol-gel citrate precursor method and characterized by FT-IR, XRD, SEM and TEM techniques and the structures of the synthesized pyranoquinoline derivatives were assigned by IR, MASS and 1 H NMR techniques. The reaction is carried out in a domestic microwave oven with a heat-resistant microwave safe glass container with a lid

Accelerator Magnet Development Based on COMB Technology with STAR Wires

This paper reports progress in the development of COMB magnet technology with STAR wires. A two-layer dipole magnet with 60 mm clear bore has been recently fabricated and tested in liquid nitrogen. The purpose of the test was to determine what kind of critical current degradation occurs in the process of winding the STAR wire into the COMB structure.Comment: CEC/ICMC2

Dynamic temporary blood facility location-allocation during and post-disaster periods

The key objective of this study is to develop a tool (hybridization or integration of different techniques) for locating the temporary blood banks during and post-disaster conditions that could serve the hospitals with minimum response time. We have used temporary blood centers, which must be located in such a way that it is able to serve the demand of hospitals in nearby region within a shorter duration. We are locating the temporary blood centres for which we are minimizing the maximum distance with hospitals. We have used Tabu search heuristic method to calculate the optimal number of temporary blood centres considering cost components. In addition, we employ Bayesian belief network to prioritize the factors for locating the temporary blood facilities. Workability of our model and methodology is illustrated using a case study including blood centres and hospitals surrounding Jamshedpur city. Our results shows that at-least 6 temporary blood facilities are required to satisfy the demand of blood during and post-disaster periods in Jamshedpur. The results also show that that past disaster conditions, response time and convenience for access are the most important factors for locating the temporary blood facilities during and post-disaster periods

Optimal methods for coordinated en-route web caching for tree networks

Web caching is an important technology for improving the scalability of Web services. One of the key problems in coordinated enroute Web caching is to compute the locations for storing copies of an object among the enroute caches so that some specified objectives are achieved. In this article, we address this problem for tree networks, and formulate it as a maximization problem. We consider this problem for both unconstrained and constrained cases. The constrained case includes constraints on the cost gain per node and on the number of object copies to be placed. We present dynamic programming-based solutions to this problem for different cases and theoretically show that the solutions are either optimal or convergent to optimal solutions. We derive efficient algorithms that produce these solutions. Based on our mathematical model, we also present a solution to coordinated enroute Web caching for autonomous systems as a natural extension of the solution for tree networks. We implement our algorithms and evaluate our model on different performance metrics through extensive simulation experiments. The implementation results show that our methods outperform the existing algorithms of either coordinated enroute Web caching for linear topology or object placement (replacement) at individual nodes only.Keqiu Li, Hong Shen, Francis Y. L. Chin, Si Qing Zhen

Coordinated Placement and Replacement for Large-Scale Distributed Caches

In a large-scale information system such as a digital library or the web, a set of distributed caches can improve their effectiveness by coordinating their data placement decisions. Using simulation, we examine three practical cooperative placement algorithms including one that is provably close to optimal, and we compare these algorithms to the optimal placement algorithm and several cooperative and non-cooperative replacement algorithms. We draw five conclusions from these experiments: (1) cooperative placement can significantly improve performance compared to local replacement algorithms particularly when the size of individual caches is limited compared to the universe of objects; (2) although the Amortized Placement algorithm is only guaranteed to be within 14 times the optimal, in practice it seems to provide an excellent approximation of the optimal; (3) in a cooperative caching scenario, the recent GreedyDual local replacement algorithm performs much better than the other local replacement algorithms; (4) our Hierarchical GreedyDual replacement algorithm yields further improvements over the GreedyDual algorithm especially when there are idle caches in the system; and (5) a key challenge to coordinated placement algorithms is generating good predictions of access patterns based on past accesses

Shares and utilities based power consolidation in virtualized server environments

Abstract—Virtualization technologies like VMware and Xen provide features to specify the minimum and maximum amount of resources that can be allocated to a virtual machine (VM) and a shares based mechanism for the hypervisor to distribute spare resources among contending VMs. However much of the existing work on VM placement and power consolidation in data centers fails to take advantage of these features. One of our experiments on a real testbed shows that leveraging such features can improve the overall utility of the data center by 47 % or even higher. Motivated by these, we present a novel suite of techniques for placement and power consolidation of VMs in data centers taking advantage of the min-max and shares features inherent in virtualization technologies. Our techniques provide a smooth mechanism for power-performance tradeoffs in modern data centers running heterogeneous applications, wherein the amount of resources allocated to a VM can be adjusted based on available resources, power costs, and application utilities. We evaluate our techniques on a range of large synthetic data center setups and a small real data center testbed comprising of VMware ESX servers. Our experiments confirm the end-to-end validity of our approach and demonstrate that our final candidate algorithm, PowerExpandMinMax, consistently yields the best overall utility across a broad spectrum of inputs – varying VM sizes and utilities, varying server capacities and varying power costs – thus providing a practical solution for administrators. I