k-server via multiscale entropic regularization

We present an $O((\log k)^2)$-competitive randomized algorithm for the $k$-server problem on hierarchically separated trees (HSTs). This is the first $o(k)$-competitive randomized algorithm for which the competitive ratio is independent of the size of the underlying HST. Our algorithm is designed in the framework of online mirror descent where the mirror map is a multiscale entropy. When combined with Bartal's static HST embedding reduction, this leads to an $O((\log k)^2 \log n)$-competitive algorithm on any $n$-point metric space. We give a new dynamic HST embedding that yields an $O((\log k)^3 \log \Delta)$-competitive algorithm on any metric space where the ratio of the largest to smallest non-zero distance is at most $\Delta$

Whatever happened to competition in space agency procurement? The case of NASA

Using the U.S. National Aeronautics and Space Administration (NASA) as a case study, this paper examines how conflicting objectives in procurement policies by public space agencies result in anti-competitive procurement. Globally, public sectors have actively encouraged mergers and acquisitions of major contractors at the national level, since the end of the “Cold War”, following largely from the perceived benefits of economies of size. The paper examines the impact the resulting industrial concentration has on the ability of space agencies to follow a pro-competitive procurement policy. Using time series econometric analysis, the paper shows that NASA’s pro-competitive policy is unsuccessful due to a shift, since the mid-1990s, in the share of appropriations in favour of its top contractors.procurement, space industry, space agencies, NASA

Online Circle and Sphere Packing

In this paper we consider the Online Bin Packing Problem in three variants: Circles in Squares, Circles in Isosceles Right Triangles, and Spheres in Cubes. The two first ones receive an online sequence of circles (items) of different radii while the third one receive an online sequence of spheres (items) of different radii, and they want to pack the items into the minimum number of unit squares, isosceles right triangles of leg length one, and unit cubes, respectively. For Online Circle Packing in Squares, we improve the previous best-known competitive ratio for the bounded space version, when at most a constant number of bins can be open at any given time, from 2.439 to 2.3536. For Online Circle Packing in Isosceles Right Triangles and Online Sphere Packing in Cubes we show bounded space algorithms of asymptotic competitive ratios 2.5490 and 3.5316, respectively, as well as lower bounds of 2.1193 and 2.7707 on the competitive ratio of any online bounded space algorithm for these two problems. We also considered the online unbounded space variant of these three problems which admits a small reorganization of the items inside the bin after their packing, and we present algorithms of competitive ratios 2.3105, 2.5094, and 3.5146 for Circles in Squares, Circles in Isosceles Right Triangles, and Spheres in Cubes, respectively

Market-Driven Management, Global Markets and Competitive Convergence

Global markets redefine competition space, fostering a collaborative network between companies (market-driven management). Globalisation it causes previously distinct global economies to converge into a single large market, thus generating fusion between competitive environments that are not only differentiated but also often very distant (competitive convergence)Competitive Convergence, Competitive Landscape, Global Competition,Global Markets