The Shapley value-probably the most important normative payoff division scheme in coalitional games-has recently been advocated as a useful measure of centrality in networks. However, although this approach has a variety of real-world applications (including social and organisational networks, biological networks and communication networks), its computational properties have not been widely studied. To date, the only practicable approach to compute Shapley value-based centrality has been via Monte Carlo simulations which are computationally expensive and not guaranteed to give an exact answer. Against this background, this paper presents the first study of the computational aspects of the Shapley value for network centralities. Specifically, we develop exact analytical formulae for Shapley value-based centrality in both weighted and unweighted networks and develop efficient (polynomial time) and exact algorithms based on them. We empirically evaluate these algorithms on two real-life examples (an infrastructure network representing the topology of the Western States Power Grid and a collaboration network from the field of astrophysics) and demonstrate that they deliver significant speedups over the Monte Carlo approach. For instance, in the case of unweighted networks our algorithms are able to return the exact solution about 1600 times faster than the Monte Carlo approximation, even if we allow for a generous 10% error margin for the latter method.

The Shapley Value is arguably the most important normative solution concept in coalitional games. One of its applications is in the domain of networks, where the Shapley Value is used to measure the relative importance of individual nodes. This measure, which is called node centrality, is of paramount significance in many real-world application domains including social and organisational networks, biological networks, communication networks and the internet. Whereas computational aspects of the Shapley Value have been analyzed in the context of conventional coalitional games, this paper presents the first such study of the Shapley Value for network centrality. Our results demonstrate that this particular application of the Shapley Value presents unique opportunities for efficiency gains, which we exploit to develop exact analytical formulas for Shapley Value based centrality computation in both weighted and unweighted networks. These formulas not only yield efficient (polynomial time) and error-free algorithms for computing node centralities, but their surprisingly simple closed form expressions also offer intuition into why certain nodes are relatively more important to a network.

No abstract

Abstract-With aggressive technology scaling and heightened variability, circuits such as SRAMs and DRAMs have become vulnerable to random telegraph noise (RTN). The bias dependence (i.e., non-stationarity), bi-directional coupling, and high inter-device variability of RTN present significant challenges to understanding its circuit-level effects. In this paper, we present two computer-aided design (CAD) tools, SAMURAI and MUS-TARD, for accurately estimating the impact of non-stationary RTN on SRAMs and DRAMs. While traditional (stationary) analysis is often overly pessimistic (e.g., it overestimates RTNinduced SRAM failure rates), the predictions made by SAMURAI and MUSTARD are more reliable by virtue of non-stationary analysis.

No abstract

No abstract

No abstract

No abstract