Virtual Network Embedding Approximations: Leveraging Randomized Rounding

© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.The Virtual Network Embedding Problem (VNEP) captures the essence of many resource allocation problems. In the VNEP, customers request resources in the form of Virtual Networks. An embedding of a virtual network on a shared physical infrastructure is the joint mapping of (virtual) nodes to physical servers together with the mapping of (virtual) edges onto paths in the physical network connecting the respective servers. This work initiates the study of approximation algorithms for the VNEP for general request graphs. Concretely, we study the offline setting with admission control: given multiple requests, the task is to embed the most profitable subset while not exceeding resource capacities. Our approximation is based on the randomized rounding of Linear Programming (LP) solutions. Interestingly, we uncover that the standard LP formulation for the VNEP exhibits an inherent structural deficit when considering general virtual network topologies: its solutions cannot be decomposed into valid embeddings. In turn, focusing on the class of cactus request graphs, we devise a novel LP formulation, whose solutions can be decomposed. Proving performance guarantees of our rounding scheme, we obtain the first approximation algorithm for the VNEP in the resource augmentation model. We propose different types of rounding heuristics and evaluate their performance in an extensive computational study. Our results indicate that good solutions can be achieved even without resource augmentations. Specifically, heuristical rounding achieves 77.2% of the baseline’s profit on average while respecting capacities.BMBF, 01IS12056, Software Campus GrantEC/H2020/679158/EU/Resolving the Tussle in the Internet: Mapping, Architecture, and Policy Making/ResolutioNe

Mobility is the Message: Experiments with Mobile Media Sharing

This thesis explores new mobile media sharing applications by building, deploying, and studying their use. While we share media in many different ways both on the web and on mobile phones, there are few ways of sharing media with people physically near us. Studied were three designed and built systems: Push!Music, Columbus, and Portrait Catalog, as well as a fourth commercially available system – Foursquare. This thesis offers four contributions: First, it explores the design space of co-present media sharing of four test systems. Second, through user studies of these systems it reports on how these come to be used. Third, it explores new ways of conducting trials as the technical mobile landscape has changed. Last, we look at how the technical solutions demonstrate different lines of thinking from how similar solutions might look today. Through a Human-Computer Interaction methodology of design, build, and study, we look at systems through the eyes of embodied interaction and examine how the systems come to be in use. Using Goffman’s understanding of social order, we see how these mobile media sharing systems allow people to actively present themselves through these media. In turn, using McLuhan’s way of understanding media, we reflect on how these new systems enable a new type of medium distinct from the web centric media, and how this relates directly to mobility. While media sharing is something that takes place everywhere in western society, it is still tied to the way media is shared through computers. Although often mobile, they do not consider the mobile settings. The systems in this thesis treat mobility as an opportunity for design. It is still left to see how this mobile media sharing will come to present itself in people’s everyday life, and when it does, how we will come to understand it and how it will transform society as a medium distinct from those before. This thesis gives a glimpse at what this future will look like

Norm varieties and algebraic cobordism

We outline briefly results and examples related with the bijectivity of the norm residue homomorphism. We define norm varieties and describe some constructions. We discuss degree formulas which form a major tool to handle norm varieties. Finally we formulate Hilbert's 90 for symbols which is the hard part of the bijectivity of the norm residue homomorphism, modulo a theorem of Voevodsky

Complex non-equilibrium dynamics in plasmas

Two new forms of strongly coupled plasmas will be discussed. They have become possible to create and observe in the laboratory only recently and exhibit a wealth of intriguing complex behavior which can be studied, in many cases for the first time, experimentally. Plasmas, gases of charged particles, are universal in the sense that certain properties of complex behavior do only depend on ratios of characteristic parameters of the plasma, not on the parameters themselves. Therefore, it is of fundamental and far reaching consequence, to be able to create and observe a strongly coupled plasma since its behavior is paradigmatic for an entire class of plasmas.Comment: 14 pages, to be published in European Revie