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Discusses problems faced with packings and embeddings of hypercubes into n-dimensional star graphs. Detailed information on packings, embeddings, and related definitions; Information on the template multiple-sized packings; Indepth look at variable-dilation embeddings (VDEs); Other related information on packings and embeddings of hypercubes.

The movement toward 3D fabrication coupled with Network-on-Chip (NoC) aims to improve area, performance, power, and scalability of many-core systems. However, reliability issue as a perpetual challenge in advanced silicon technology imperils it. Aging is an emerging reliability concern, which degrades the system's performance and causes timing failure eventually. Bias-Temperature-Instability (BTI) and Hot-Carrier-Injection (HCI) are the dominant aging mechanisms, which escalate in high temperature and stress (i.e., usage). In addition to the intra-layer temperature variations, 3D NoCs experience inter-layer temperature variations, which demand necessary investigations for aging as compared to 2D NoC. In this paper, we propose AROMa, an aging-aware deadlock-free adaptive routing algorithm integrated with a novel online aging monitoring system for 3D NoCs. The monitoring system in AROMa exploits Distributed-Centralized-Aging-Table (D-CAT) to obtain routers’ aging rates for each layer of 3D NoCs periodically. Consequently, AROMa swaps between different k-best source-destination shortest paths periodically to avoid highly aged routers, force them in recovery phase of BTI, and accordingly balance aging in the network. We prove that AROMa is deadlock free. Our extensive experimental analysis using gem5 full system mode for PARSEC and SPLASH-2 benchmark suites concludes that AROMa outperforms state-of-the-art works while improving age imbalance by 70 percent and maximum age by 35 percent in 3D NoC with negligible overheads. [ABSTRACT FROM AUTHOR]

Recently, Through-Silicon-Via (TSV) has been more popular to provide faster inter-layer communication in three-dimensional Networks-on-Chip (3D NoCs). However, the area overhead of TSVs reduces wafer utilization and yield which impact design of 3D architectures using a large number of TSVs such as homogeneous 3D NoCs topologies. Also, 3D routers require more memory and thus they are more power hungry than conventional 2D routers. Alternatively, hybrid 3D NoCs combine both the area and performance benefits of 2D and 3D router architectures by using a limited number of TSVs. Existing hybrid architectures suffer from higher packet delays as they do not consider the dynamic communication patterns of different application and their NoC resource usage. We propose a novel algorithm to systematically generate hybrid 3D NoC topologies for a given application such that the vertical connections are minimized while the NoC performance is not sacrificed. The proposed algorithm analyses the target application and generates hybrid architectures by efficiently redistributing the vertical links and buffer spaces based on their utilizations. Furthermore, the algorithm has been evaluated with synthetic and various real-world traffic patterns. Experimental results show that the proposed algorithm generates optimized architectures with lower energy consumption and a significant reduction in packet delay compared to the existing solutions. [ABSTRACT FROM PUBLISHER]