On Eulerian orientations of even-degree hypercubes

The final publication is available at Elsevier via https://dx.doi.org/10.1016/j.orl.2018.09.002 © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/It is well known that every Eulerian orientation of an Eulerian 2k-edge connected (undirected) graph is strongly k-edge connected. A long-standing goal in the area is to obtain analogous results for other types of connectivity, such as node connectivity. We show that every Eulerian orientation of the hypercube of degree 2k is strongly k-node connected.Natural Sciences and Engineering Research Council of Canada ["RGPIN–2014–04351"

MCFlow: Middleware for Mixed-Criticality Distributed Real-Time Systems

Traditional fixed-priority scheduling analysis for periodic/sporadic task sets is based on the assumption that all tasks are equally critical to the correct operation of the system. Therefore, every task has to be schedulable under the scheduling policy, and estimates of tasks\u27 worst case execution times must be conservative in case a task runs longer than is usual. To address the significant under-utilization of a system\u27s resources under normal operating conditions that can arise from these assumptions, several \emph{mixed-criticality scheduling} approaches have been proposed. However, to date there has been no quantitative comparison of system schedulability or run-time overhead for the different approaches. In this dissertation, we present what is to our knowledge the first side-by-side implementation and evaluation of those approaches, for periodic and sporadic mixed-criticality tasks on uniprocessor or distributed systems, under a mixed-criticality scheduling model that is common to all these approaches. To make a fair evaluation of mixed-criticality scheduling, we also address some previously open issues and propose modifications to improve schedulability and correctness of particular approaches. To facilitate the development and evaluation of mixed-criticality applications, we have designed and developed a distributed real-time middleware, called MCFlow, for mixed-criticality end-to-end tasks running on multi-core platforms. The research presented in this dissertation provides the following contributions to the state of the art in real-time middleware: (1) an efficient component model through which dependent subtask graphs can be configured flexibly for execution within a single core, across cores of a common host, or spanning multiple hosts; (2) support for optimizations to inter-component communication to reduce data copying without sacrificing the ability to execute subtasks in parallel; (3) a strict separation of timing and functional concerns so that they can be configured independently; (4) an event dispatching architecture that uses lock free algorithms where possible to reduce memory contention, CPU context switching, and priority inversion; and (5) empirical evaluations of MCFlow itself and of different mixed criticality scheduling approaches both with a single host and end-to-end across multiple hosts. The results of our evaluation show that in terms of basic distributed real-time behavior MCFlow performs comparably to the state of the art TAO real-time object request broker when only one core is used and outperforms TAO when multiple cores are involved. We also identify and categorize different use cases under which different mixed criticality scheduling approaches are preferable

Uni-Directional Alternating Group Graphs

A class of uni-directional Cayley graphs based on alternating groups is proposed in this paper. It is shown that this class of graphs is strongly connected and recursively scalable. The analysis of the shortest distance between any pair of nodes in a graph of this class is also given. Based on the analysis, we develop a polynomial time routing algorithm which yields a path distance at most one more than the theoretic lower bound. Furthermore, comparisons among uni-directional hypercubes, uni-directional star graphs, and uni-directional alternating group graphs are given. These observations validate the superiority of uni-directional alternating group graphs among known uni-directional topologies