Improving Efficiency and Effectiveness of Multipath Routing in Computer Networks

In this dissertation, we studied methods for improving efficiency and effectiveness of multipath routing in computer networks. We showed that multipath routing can improve network performance for failure recovery, load balancing, Quality of Service (QoS), and energy consumption. We presented a method for reducing the overhead of computing dynamic path metrics, one of the obstacles for implementing dynamic multipath routing in real world networks. In the first part, we proposed a method for building disjoint multipaths that could be used for local failure recovery as well as for multipath routing. Proactive failure recovery schemes have been recently proposed for continuous service of delay-sensitive applications during failure transients at the cost of extra infrastructural support in the form of routing table entries, extra addresses, etc. These extra infrastructure supports could be exploited to build alternative disjoint paths in those frameworks, while keeping the lengths of the alternative paths close to those of the primary paths. The evaluations showed that it was possible to extend the proactive failure recovery schemes to provide support for nearly-disjoint paths which could be employed in multipath routing for load balancing and QoS. In the second part, we proposed a method for reducing overhead of measuring dynamic link state information for multipath routing, specifically path delays used in Wardrop routing. Even when dynamic routing could be shown to offer convergence properties without oscillations, it has not been widely adopted. One of reasons was that the expected cost of keeping the link metrics updated at various nodes in the network. We proposed threshold-based updates to propagate the link state only when the currently measured link state differs from the last updated state consider- ably. Threshold-based updates were shown through analysis and simulations to offer bounded guarantees on path quality while significantly reducing the cost of propagating the dynamic link metric information. The simulation studies indicated that threshold based updates can reduce the number of link updates by up to 90-95% in some cases. In the third part, we proposed methods of using multipath routing for reducing energy consumption in computer networks. Two different approaches have been advocated earlier, from traffic engineering and topology control to hardware-based approaches. We proposed solutions at two different time scales. On a finer time granularity, we employed a method of forwarding through alternate paths to enable longer sleep schedules of links. The proposed schemes achieved more energy saving by increasing the usage of active links and the down time of sleeping links as well as avoiding too frequent link state changes. To the best of our knowledge, this was the first technique combining a routing scheme with hardware scheme to save energy consumption in networks. In our evaluation, alternative forwarding reduced energy consumption by 10% on top of a hardware-based sleeping scheme. On a longer time granularity, we proposed a technique that combined multipath routing with topology control. The proposed scheme achieved increased energy savings by maximizing the link utilization on a reduced topology where the number of active nodes and links are minimized. The proposed technique reduced energy consumption by an additional 17% over previous schemes with single/shortest path routing

Optimal Gaussian measurements for phase estimation in single-mode Gaussian metrology

The central issue in quantum parameter estimation is to find out the optimal measurement setup that leads to the ultimate lower bound of an estimation error. We address here a question of whether a Gaussian measurement scheme can achieve the ultimate bound for phase estimation in single-mode Gaussian metrology that exploits single-mode Gaussian probe states in a Gaussian environment. We identify three types of optimal Gaussian measurement setups yielding the maximal Fisher information depending on displacement, squeezing, and thermalization of the probe state. We show that the homodyne measurement attains the ultimate bound for both displaced thermal probe states and squeezed vacuum probe states, whereas for the other single-mode Gaussian probe states, the optimized Gaussian measurement cannot be the optimal setup, although they are sometimes nearly optimal. We then demonstrate that the measurement on the basis of the product quadrature operators XP+PX, i.e., a non-Gaussian measurement, is required to be fully optimal.Comment: 13 pages, 6 figure

Smooth constructions of homotopy-coherent actions

We prove that, for nice classes of infinite-dimensional smooth groups G, natural constructions in smooth topology and symplectic topology yield homotopically coherent group actions of G. This yields a bridge between infinite-dimensional smooth groups and homotopy theory. The result relies on two computations: One showing that the diffeological homotopy groups of the Milnor classifying space BG are naturally equivalent to the (continuous) homotopy groups, and a second showing that a particular strict category localizes to yield the homotopy type of BG. We then prove a result in symplectic geometry: These methods are applicable to the group of Liouville automorphisms of a Liouville sector. The present work is written with an eye toward [OT19], where our constructions show that higher homotopy groups of symplectic automorphism groups map to Fukaya-categorical invariants, and where we prove a conjecture of Teleman from the 2014 ICM in the Liouville and monotone settings.Comment: 23 pages. Comments welcome! Portions of this work previously appeared in arXiv:1911.00349v2; that previous work has been split into multiple papers (including this one) to better explicate the ingredient