Tight Analysis of a Multiple-Swap Heuristic for Budgeted Red-Blue Median

Budgeted Red-Blue Median is a generalization of classic $k$-Median in that there are two sets of facilities, say $\mathcal{R}$ and $\mathcal{B}$, that can be used to serve clients located in some metric space. The goal is to open $k_r$ facilities in $\mathcal{R}$ and $k_b$ facilities in $\mathcal{B}$ for some given bounds $k_r, k_b$ and connect each client to their nearest open facility in a way that minimizes the total connection cost. We extend work by Hajiaghayi, Khandekar, and Kortsarz [2012] and show that a multiple-swap local search heuristic can be used to obtain a $(5+\epsilon)$-approximation for Budgeted Red-Blue Median for any constant $\epsilon > 0$. This is an improvement over their single swap analysis and beats the previous best approximation guarantee of 8 by Swamy [2014]. We also present a matching lower bound showing that for every $p \geq 1$, there are instances of Budgeted Red-Blue Median with local optimum solutions for the $p$-swap heuristic whose cost is $5 + \Omega\left(\frac{1}{p}\right)$ times the optimum solution cost. Thus, our analysis is tight up to the lower order terms. In particular, for any $\epsilon > 0$ we show the single-swap heuristic admits local optima whose cost can be as bad as $7-\epsilon$ times the optimum solution cost

Ultrasonic monitoring of temperature distributions and degradation in engineering components

Material degradations such as corrosion and erosion are prevalent in facilities of the energy sector. Excessive and unexpected material degradations can lead to catastrophic structure failures, severe service disruption and even loss of lives. Ultrasound-based non-destructive evaluation (NDE) and structural health monitoring (SHM) technology has been developed to provide quantitative data to monitor degradation processes so that they can be mitigated in the best possible way. This thesis aims to improve these ultrasound-based NDE and SHM methods by reducing their uncertainties and exploring their potential applications on emerging technologies. The first part of the thesis focuses on advancing temperature compensation strategies of the NDE and SHM technology. This is because environmental and operational conditions (EOCs), especially temperature changes are one of the biggest sources of uncertainties in the current ultrasonic measurements. At the same time, temperature controls the rate of various electrochemical processes and therefore influences the rate of material degradation. A novel dual-wave approach is presented to enhance the performance of the existing monitoring technology. By exciting both shear and longitudinal waves at the same location of a component, variations of component thickness and internal temperature distributions can be simultaneously monitored. It was shown that even under drastic thermal swings (40 celsius temperature change in under 3 minutes), thickness variations of 2 micrometers can be accurately tracked. Compared with the existing single-wave approach, thickness measurement errors can be reduced by a factor of 5. At the same time, ultrasonic temperature predictions agreed with the independent measurements using a resistance temperature detector (RTD) to within 2 celsius and corrosion-induced temperature prediction drift can be reduced by a factor of 9. The second part of the thesis explores the possibility of applying ultrasonic NDE and SHM technology on monitoring degradation phenomena in energy storage systems (ESS). ESS such as batteries have seen rapid developments recently due to the emerging demand to store energy produced from renewable resources. However, these devices also suffer from degradation issues and require appropriate monitoring solutions. This work targets a specific battery degradation phenomenon - dendrite growth at the electrode/electrolyte interface. A novel measurement method is proposed which can excite the SH0* mode guided wave in a waveguide that also serves as the battery electrode. Experimental investigations demonstrated the feasibility of the approach. The SH0* mode guided wave was shown to be sensitive to zinc dendrite in the order of tens of micrometres. Moreover, the results revealed correlations between ultrasonic signal variations and the underlying zinc plating/stripping processes, thus providing more physical insights into battery degradation mechanisms.Open Acces

Breaking the challenge of signal integrity using time-domain spoof surface plasmon polaritons

In modern integrated circuits and wireless communication systems/devices, three key features need to be solved simultaneously to reach higher performance and more compact size: signal integrity, interference suppression, and miniaturization. However, the above-mentioned requests are almost contradictory using the traditional techniques. To overcome this challenge, here we propose time-domain spoof surface plasmon polaritons (SPPs) as the carrier of signals. By designing a special plasmonic waveguide constructed by printing two narrow corrugated metallic strips on the top and bottom surfaces of a dielectric substrate with mirror symmetry, we show that spoof SPPs are supported from very low frequency to the cutoff frequency with strong subwavelength effects, which can be converted to the time-domain SPPs. When two such plasmonic waveguides are tightly packed with deep-subwavelength separation, which commonly happens in the integrated circuits and wireless communications due to limited space, we demonstrate theoretically and experimentally that SPP signals on such two plasmonic waveguides have better propagation performance and much less mutual coupling than the conventional signals on two traditional microstrip lines with the same size and separation. Hence the proposed method can achieve significant interference suppression in very compact space, providing a potential solution to break the challenge of signal integrity

A universal approach to coverage probability and throughput analysis for cellular networks

This paper proposes a novel tractable approach for accurately analyzing both the coverage probability and the achievable throughput of cellular networks. Specifically, we derive a new procedure referred to as the equivalent uniformdensity plane-entity (EUDPE)method for evaluating the other-cell interference. Furthermore, we demonstrate that our EUDPE method provides a universal and effective means to carry out the lower bound analysis of both the coverage probability and the average throughput for various base-station distribution models that can be found in practice, including the stochastic Poisson point process (PPP) model, a uniformly and randomly distributed model, and a deterministic grid-based model. The lower bounds of coverage probability and average throughput calculated by our proposed method agree with the simulated coverage probability and average throughput results and those obtained by the existing PPP-based analysis, if not better. Moreover, based on our new definition of cell edge boundary, we show that the cellular topology with randomly distributed base stations (BSs) only tends toward the Voronoi tessellation when the path-loss exponent is sufficiently high, which reveals the limitation of this popular network topology