Path computation in multi-layer networks: Complexity and algorithms

Carrier-grade networks comprise several layers where different protocols coexist. Nowadays, most of these networks have different control planes to manage routing on different layers, leading to a suboptimal use of the network resources and additional operational costs. However, some routers are able to encapsulate, decapsulate and convert protocols and act as a liaison between these layers. A unified control plane would be useful to optimize the use of the network resources and automate the routing configurations. Software-Defined Networking (SDN) based architectures, such as OpenFlow, offer a chance to design such a control plane. One of the most important problems to deal with in this design is the path computation process. Classical path computation algorithms cannot resolve the problem as they do not take into account encapsulations and conversions of protocols. In this paper, we propose algorithms to solve this problem and study several cases: Path computation without bandwidth constraint, under bandwidth constraint and under other Quality of Service constraints. We study the complexity and the scalability of our algorithms and evaluate their performances on real topologies. The results show that they outperform the previous ones proposed in the literature.Comment: IEEE INFOCOM 2016, Apr 2016, San Francisco, United States. To be published in IEEE INFOCOM 2016, \<http://infocom2016.ieee-infocom.org/\&g

Structural parameterizations for boxicity

The boxicity of a graph $G$ is the least integer $d$ such that $G$ has an intersection model of axis-aligned $d$-dimensional boxes. Boxicity, the problem of deciding whether a given graph $G$ has boxicity at most $d$, is NP-complete for every fixed $d \ge 2$. We show that boxicity is fixed-parameter tractable when parameterized by the cluster vertex deletion number of the input graph. This generalizes the result of Adiga et al., that boxicity is fixed-parameter tractable in the vertex cover number. Moreover, we show that boxicity admits an additive $1$-approximation when parameterized by the pathwidth of the input graph. Finally, we provide evidence in favor of a conjecture of Adiga et al. that boxicity remains NP-complete when parameterized by the treewidth.Comment: 19 page

Turbo-Aggregate: Breaking the Quadratic Aggregation Barrier in Secure Federated Learning

Federated learning is a distributed framework for training machine learning models over the data residing at mobile devices, while protecting the privacy of individual users. A major bottleneck in scaling federated learning to a large number of users is the overhead of secure model aggregation across many users. In particular, the overhead of the state-of-the-art protocols for secure model aggregation grows quadratically with the number of users. In this paper, we propose the first secure aggregation framework, named Turbo-Aggregate, that in a network with $N$ users achieves a secure aggregation overhead of $O(N\log{N})$, as opposed to $O(N^2)$, while tolerating up to a user dropout rate of $50\%$. Turbo-Aggregate employs a multi-group circular strategy for efficient model aggregation, and leverages additive secret sharing and novel coding techniques for injecting aggregation redundancy in order to handle user dropouts while guaranteeing user privacy. We experimentally demonstrate that Turbo-Aggregate achieves a total running time that grows almost linear in the number of users, and provides up to $40\times$ speedup over the state-of-the-art protocols with up to $N=200$ users. Our experiments also demonstrate the impact of model size and bandwidth on the performance of Turbo-Aggregate

Goat and cow casein derived ingredients and their interactions with iron : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Food Technology, Massey University, Palmerston North, New Zealand

The objective of this study was to gain a fundamental understanding of how goat casein micelles and the products of casein proteins behave when fortified with iron. Iron fortified skim milk was characterised by analysing the mass balance of micellar/non micellar fractions, chemical changes, micellar size changes and internal structure. Two treatments were examined to determine where in the processing line the addition of iron might best be added to a milk system. On average, at least 72% of the iron is bound to the micellar phase across the treatments and iron concentrations. Small angle X-ray scattering (SAXS) indicated that internal changes, mainly at the location of the colloidal calcium phosphate, occurred with iron addition. Casein was extracted from goat milk using isoelectric precipitation however the extraction was more difficult than using cow milk. Iron fortification of the caseinates resulted in a tendency for oxidation and precipitation of the proteins to occur causing the formation of large aggregates. The caseinates could not stabilise the same amounts of iron to that of an intact casein micelle. Phosphopeptides were isolated by adding calcium and ethanol to caseinate digests. There was an increase in serine, glutamic acid and isoleucine residues compared to caseinate. There was an increase in phosphorus from 7.8 ± 0.3 mg P/ g solids to 45.4 ± 2.4 mg P/ g solids in the isolate. The phosphopeptides were composed of smaller, more hydrophilic peptides compared to the full digest prior to precipitation. Ferrous sulfate was then investigated for use as the precipitant, instead of calcium. The peptides produced similar trends in terms of amino acid profile changes, phosphorus concentration increase and yield. Immobilised metal affinity chromatography was also investigated however this had a low throughput that may not be effective at process scale. The effect of heating, cooling, ionic strength of the solution, holding time, iron loading, processing order and use in a model milk system were investigated to simulate potential industrial processing conditions using the calcium - extracted phosphopeptides. It was found that goat peptide isolates were able to bind 54.4 ± 0.5 mg Fe/ g protein compared to goat milk of 4.3 ± 0.1 mg Fe/ g protein. The optimal conditions for binding were found to be at pH 6.7 in a low ionic strength solution, around 37 oC. There was a potential synergistic effect of adding the peptides to milk in terms of iron binding capacity. There were few differences in the amount of iron that could be bound comparing cow and goat derived phosphopeptides under the tested conditions. The oxidation potential of ingredients was determined using malondialdehyde (MDA) as an oxidation product marker. There was a reduction in oxidation when iron was bound to milk or peptides compared to free ferrous sulfate in solution with intact goat milk performing the best producing 0.46 ± 0.04 μg MDA/mL after 3 days at 30 oC compared to the blank of 1.25 ± 0.16 μg MDA/mL. The goat peptides produced non-significantly different levels of MDA compared to the blank containing no ferrous sulfate. Caco-2 cell lines are a way of approximating how systems may function in an intestine in terms of nutrient absorption. Iron absorption was improved in the order of casein hydrolysates > caseinate > skim milk for goat milk. In contrast, cow milk appeared to perform better without any modifications to the proteins. On an equal iron filtrate basis after the digestion and intestinal phase, calcium- precipitated goat phosphopeptides produced a response of 9.64 ± 0.94 ng ferritin/ nM iron. This response was greater than all other treatments with the exception of goat milk fortified with 5 mM iron and ascorbic acid with 12.30 ± 1.23 ng ferritin/ nM iron. This work covers a wide range of milk products and iron interactions and has helped to build a fundamental understanding of goat milk protein functionality. The underpinning considerations to a manufacturing setting may allow further development of large scale ingredient production for the improved stability of iron fortified systems