Hypergraph Partitioning Algorithms

We present the first polynomial time approximation algorithms for the balanced hypergraph partitioning problem. The approximations are within polylogarithmic factors of the optimal solutions. The choice of algorithm involves a time complexity/approximation bound tradeoff. We employ a two step methodology. First we approximate the flux of the input hypergraph. This involves an approximate solution to a concurrent flow problem on the hypergraph. In the second step we use the approximate flux to obtain approximations for the balanced bipartitioning problem. Our results extend the approximation algorithms by Leighton-Rao on graphs to hypergraphs. We also give the first polylogarithmic times optimal approximation algorithms for multiway (graph and hypergraph) partitioning problems into bounded size sets. A better approximation algorithm for the latter problem is finally presented for the special case of bounded sets of size at most O(log n) on planar graphs and hypergraphs, where n is the number of nodes of the input instance

Tight Bounds for On-line Tree Embedding

Many tree–structured computations are inherently parallel. As leaf processes are recursively spawned they can be assigned to independent processors in a multicomputer network. To maintain load balance, an on–line mapping algorithm must distribute processes equitably among processors. Additionally, the algorithm itself must be distributed in nature, and process allocation must be completed via message–passing with minimal communication overhead. This paper investigates bounds on the performance of deterministic and randomized algorithms for on–line tree embedding. In particular, we study tradeoffs between performance (load–balance) and communication overhead (message congest ion). We give a simple technique to derive lower bounds on the congestion that any on–line allocation algorithm must incur in order to guarantee load balance. This technique works for both randomized and deterministic algorithms, although we find that the performance of randomized on-line algorithms to be somewhat better than that of deterministic algorithms. Optimal bounds are achieved for several networks including multi–dimensional grids and butterflies

Basic Network Creation Games

We study a natural network creation game, in which each node locally tries to minimize its local diameter or its local average distance to other nodes, by swapping one incident edge at a time. The central question is what structure the resulting equilibrium graphs have, in particular, how well they globally minimize diameter. For the local-average-distance version, we prove an upper bound of 2O(√ lg n), a lower bound of 3, a tight bound of exactly 2 for trees, and give evidence of a general polylogarithmic upper bound. For the local-diameter version, we prove a lower bound of Ω(√ n), and a tight upper bound of 3 for trees. All of our upper bounds apply equally well to previously extensively studied network creation games, both in terms of the diameter metric described above and the previously studied price of anarchy (which are related by constant factors). In surprising contrast, our model has no parameter α for the link creation cost, so our results automatically apply for all values of alpha without additional effort; furthermore, equilibrium can be checked in polynomial time in our model, unlike previous models. Our perspective enables simpler and more general proofs that get at the heart of network creation games

Automatic Methods for Hiding Latency in Parallel and Distributed Computation

In this paper we describe methods for mitigating the degradation in performance caused by high latencies in parallel and distributed networks. For example, given any dataflow type of algorithm that runs in T steps on an n-node ring with unit link delays, we show how to run the algorithm in O(T) steps on any n-node bounded-degree connected network with average link delay O(1). This is a significant improvement over prior approaches to latency hiding, which require slowdowns proportional to the maximum link delay. In the case when the network has average link delay dave, our simulation runs in O(√daveT) steps using n/√dave processors, thereby preserving efficiency. We also show how to efficiently simulate an n × n array with unit link delays using slowdown Õ (d&frac23ave) on a two-dimensional array with average link delay dave. Last, we present results for the case in which large local databases are involved in the computation

Whittier Homeownership Center Targeting Project.

Prepared for Whittier Alliance, 612/871-7756. Sponsored by Neighborhood Planning for Community Revitalization, Center for Urban and Regional Affairs, University of Minnesota

Two-layer viscous instability in a rotating couette device

A novel experiment to study the interfacial shear instability between two liquids is described. Density-matched immiscible liquids are confined between concentric cylinders such that the interface is parallel to the cylinder walls. Interfacial waves that develop because of viscosity differences between the shearing fluids are studied as a function of rotation rate and depth ratio using optical techniques. Conditions neutral stability and the most unstable wavenumber agree reasonably well with predictions from linear stability analysis of the Navier-Stokes equations. Illumination using laser sheets allows precise measurement of the interface shape. Future experiments will verify the correctness of weakly nonlinear theories that describe energy transfer and saturation of wave growth by nonlinear effects. Measurements of solitary wave shapes, that occur far above neutral stability, will be compared to similar measurements for systems that have gravity as an important force to determine how gravity effects large disturbances. These results will be used to interpret slug and annular flow data that have been obtained in other mu g studies

Pesticide spraying for West Nile virus control and emergency department asthma visits in New York City, 2000

Pyrethroid pesticides were applied via ground spraying to residential neighborhoods in New York City during July–September 2000 to control mosquito vectors of West Nile virus (WNV). Case reports link pyrethroid exposure to asthma exacerbations, but population-level effects on asthma from large-scale mosquito control programs have not been assessed. We conducted this analysis to determine whether widespread urban pyrethroid pesticide use was associated with increased rates of emergency department (ED) visits for asthma. We recorded the dates and locations of pyrethroid spraying during the 2000 WNV season in New York City and tabulated all ED visits for asthma to public hospitals from October 1999 through November 2000 by date and ZIP code of patients’ residences. The association between pesticide application and asthma-related emergency visits was evaluated across date and ZIP code, adjusting for season, day of week, and daily temperature, precipitation, particulate, and ozone levels. There were 62,827 ED visits for asthma during the 14-month study period, across 162 ZIP codes. The number of asthma visits was similar in the 3-day periods before and after spraying (510 vs. 501, p = 0.78). In multivariate analyses, daily rates of asthma visits were not associated with pesticide spraying (rate ratio = 0.92; 95% confidence interval, 0.80–1.07). Secondary analyses among children and for chronic obstructive pulmonary disease yielded similar null results. This analysis shows that spraying pyrethroids for WNV control in New York City was not followed by population-level increases in public hospital ED visit rates for asthma