Generalized Assignment via Submodular Optimization with Reserved Capacity

We study a variant of the generalized assignment problem (GAP) with group constraints. An instance of (Group GAP) is a set I of items, partitioned into L groups, and a set of m uniform (unit-sized) bins. Each item i in I has a size s_i >0, and a profit p_{i,j} >= 0 if packed in bin j. A group of items is satisfied if all of its items are packed. The goal is to find a feasible packing of a subset of the items in the bins such that the total profit from satisfied groups is maximized. We point to central applications of Group GAP in Video-on-Demand services, mobile Device-to-Device network caching and base station cooperation in 5G networks. Our main result is a 1/6-approximation algorithm for Group GAP instances where the total size of each group is at most m/2. At the heart of our algorithm lies an interesting derivation of a submodular function from the classic LP formulation of GAP, which facilitates the construction of a high profit solution utilizing at most half the total bin capacity, while the other half is reserved for later use. In particular, we give an algorithm for submodular maximization subject to a knapsack constraint, which finds a solution of profit at least 1/3 of the optimum, using at most half the knapsack capacity, under mild restrictions on element sizes. Our novel approach of submodular optimization subject to a knapsack with reserved capacity constraint may find applications in solving other group assignment problems

Analysing randomised controlled trials with missing data : Choice of approach affects conclusions

Copyright © 2012 Elsevier Inc. All rights reserved. PMID: 22265924 [PubMed - indexed for MEDLINE]Peer reviewedPostprin

No reserved communication lanes for high energy

The American particle physics community is in jeopardy and may end up drowning in a boundless sea trying to grasp at non-existing funds, dragging US physics and science as a whole to the bottom. This is a price the most powerful and high-tech country of the world cannot afford, as warned by the editors of a report published in late April by the National Academy of Sciences1. Behind so much alarm is the International Linear Collider (ILC) – a large particle accelerator facility which, according to the report, should be built on American territory, if research on the elementary constituents of nature is to survive in the United States. The ILC will probably cost a total of five hundred million dollars in the first five years, whereas billions will have to be invested in the subsequent seven years. Hardly impressive, however, if compared with the Superconducting Super Collider (SSC), the biggest and costliest machine ever conceived in the history of science. Devised to describe the first instants of the universe, as many will recall, the SSC project was severely hampered by political and bureaucratic plots in 1993, when the Clinton administration decided to halt work on the accelerator, after ten years and approximately two billion dollars already spent

Is There a Federal Definitions Power?

Although the Supreme Court decided United States v. Windsor on equal protection grounds, that case also raised important and recurring questions about federal power. In particular, defenders of the Defense of Marriage Act (DOMA) argued that Congress may always define the terms used in federal statutes, even if its definition concerns a matter reserved to the States. As the DOMA illustrates, federal definitions concerning reserved matters that depart from state law may impose significant burdens on state governments and private citizens alike. This Article argues that there is no general, freestanding federal definitions power and that sometimes—as with marriage—federal law must incorporate state law definitions

Neuromodulation

Neuromodulation is a new promising treatment for headache disorders. It consists of peripheral nerve neurostimulation and central neurostimulation. © 2016, Touch Briefings. All rights reserved