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Given a network and a set of connection requests on it, we consider the maximum edge-disjoint paths and related generalizations and routing problems that arise in assigning paths for these requests. We present improved approximation algorithms and/or integrality gaps for all problems considered; the central theme of this work is the underlying multi-commodity flow relaxation. Applications of these techniques to approximating families of packing integer programs are also presented.

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A logical strategy to contain the Covid-19 pandemic is to completely isolate everyone for 2 weeks (the incubation period of the virus). However, such a strategy can have prohibitive economic and social costs and, therefore, will be difficult to implement. At the same time, the current situation is leading to an expanding humanitarian, health and economic crisis. Based on principles of the Theory of Constraints, we propose in this article the "Shutting-down Transmission Of Pandemic" (STOP Covid-19) plan that would reliably contain the pandemic, mitigate its economic consequences, and boost societal confidence. This plan requires the implementation of four strategies over 90 days: (a) stop all international, domestic passenger air and intercity bus/train travel; (b) create administrative zones of about 1 million people; (c) stop all non-emergency cross-zonal travel except for transportation of goods, and (d) deploy an information-driven service value chain to control the spread of the pandemic within a zone.Keywords Covid-19 · Service value chain · Supply chain management · Theory of constraints · Pandemic management Left to its own progression the Covid-19 pathogen could spread through the world population following a logistic curve (Sanderson 2020). As can be seen from Fig. 1, in the first half of the progression, there is an exponential growth in the number of infections. The rate of growth is determined by the average number of susceptible people exposed to the pathogen by a typical infected person during their infectious phase. The spread of the virus quickens as the value of the transmission rate increases. As the number of infected people increases, the number of uninfected people declines, and the rate of growth of infections will start to reduce progressively. By the saturation point of the contagion, almost everyone would have been infected. To put this in perspective, assuming a 1% mortality rate and no seasonal effects of virus prevalence and virulence, there would be about 70 million deaths, worldwide,