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Cominetti, R., Dose, V., & Scarsini, M. (2022). The price of anarchy in routing games as a function of the demand. Math. Program., Early Access.
Abstract: The price of anarchy has become a standard measure of the efficiency of equilibria in games. Most of the literature in this area has focused on establishing worst-case bounds for specific classes of games, such as routing games or more general congestion games. Recently, the price of anarchy in routing games has been studied as a function of the traffic demand, providing asymptotic results in light and heavy traffic. The aim of this paper is to study the price of anarchy in nonatomic routing games in the intermediate region of the demand. To achieve this goal, we begin by establishing some smoothness properties of Wardrop equilibria and social optima for general smooth costs. In the case of affine costs we show that the equilibrium is piecewise linear, with break points at the demand levels at which the set of active paths changes. We prove that the number of such break points is finite, although it can be exponential in the size of the network. Exploiting a scaling law between the equilibrium and the social optimum, we derive a similar behavior for the optimal flows. We then prove that in any interval between break points the price of anarchy is smooth and it is either monotone (decreasing or increasing) over the full interval, or it decreases up to a certain minimum point in the interior of the interval and increases afterwards. We deduce that for affine costs the maximum of the price of anarchy can only occur at the break points. For general costs we provide counterexamples showing that the set of break points is not always finite.
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Nafees, N., Ahmed, S., Kakkar, V., Bahar, A. N., Wahid, K. A., & Otsuki, A. (2022). QCA-Based PIPO and SIPO Shift Registers Using Cost-Optimized and Energy-Efficient D Flip Flop. Electronics, 11(19), 3237.
Abstract: With the growing use of quantum-dot cellular automata (QCA) nanotechnology, digital circuits designed at the Nanoscale have a number of advantages over CMOS devices, including the lower utilization of power, increased processing speed of the circuit, and higher density. There are several flip flop designs proposed in the literature with their realization in the QCA technology. However, the majority of these designs suffer from large cell counts, large area utilization, and latency, which leads to the high cost of the circuits. To address this, this work performed a literature survey of the D flip flop (DFF) designs and complex sequential circuits that can be designed from it. A new design of D flip flop was proposed in this work and to assess the performance of the proposed QCA design, an in-depth comparison with existing designs was performed. Further, sequential circuits such as parallel-in-parallel-out (PIPO) and serial-in-parallel-out (SIPO) shift registers were designed using the flip flop design that was put forward. A comprehensive evaluation of the energy dissipation of all presented fundamental flip-flop circuits and other sequential circuits was also performed using the QCAPro tool, and their energy dissipation maps were also obtained. The suggested designs showed lower power dissipation and were cost-efficient, making them suitable for designing higher-power circuits.
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Vahabi, M., Bahar, A. N., Otsuki, A., & Wahid, K. A. (2022). Ultra-Low-Cost Design of Ripple Carry Adder to Design Nanoelectronics in QCA Nanotechnology. Electronics, 11(15), 2320.
Abstract: Due to the development of integrated circuits and the lack of responsiveness to existing technology, researchers are looking for an alternative technology. Quantum-dot cellular automata (QCA) technology is one of the promising alternatives due to its higher switch speed, lower power dissipation, and higher device density. One of the most important and widely used circuits in digital logic calculations is the full adder (FA) circuit, which actually creates the problem of finding its optimal design and increasing performance. In this paper, we designed and implemented two new FA circuits in QCA technology and then implemented ripple carry adder (RCA) circuits. The proposed FAs and RCAs showed excellent performance in terms of QCA evaluation parameters, especially in cost and cost function, compared to the other reported designs. The proposed adders' approach was 46.43% more efficient than the best-known design, and the reason for this superiority was due to the coplanar form, without crossovers and inverter gates in the designs.
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