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Finding connected components in a graph is a fundamental problem in graph analysis. In this work, we present a novel minimum-mapping based Contour algorithm to efficiently solve the connectivity problem. We prove that the Contour algorithm with two or higher order operators can identify all connected components of an undirected graph within $\mathcal{O}(\log d_{max})$ iterations, with each iteration involving $\mathcal{O}(m)$ work, where $d_{max}$ represents the largest diameter among all components in the given graph, and $m$ is the total number of edges in the graph. Importantly, each iteration is highly parallelizable, making use of the efficient minimum-mapping operator applied to all edges. To further enhance its practical performance, we optimize the Contour algorithm through asynchronous updates, early convergence checking, eliminating atomic operations, and choosing more efficient mapping operators. Our implementation of the Contour algorithm has been integrated into the open-source framework Arachne. Arachne extends Arkouda for large-scale interactive graph analytics, providing a Python API powered by the high-productivity parallel language Chapel. Experimental results on both real-world and synthetic graphs demonstrate the superior performance of our proposed Contour algorithm compared to state-of-the-art large-scale parallel algorithm FastSV and the fastest shared memory algorithm ConnectIt. On average, Contour achieves a speedup of 7.3x and 1.4x compared to FastSV and ConnectIt, respectively. All code for the Contour algorithm and the Arachne framework is publicly available on GitHub ( https://github.com/Bears-R-Us/arkouda-njit ), ensuring transparency and reproducibility of our work., Comment: 30th IEEE International Conference on High Performance Computing, Data, and Analytics, Goa, India, December 2023

In order to address the need for more capacity and coverage in the 5th generation (5G) of wireless networks, ultra-dense wireless networks are introduced which mainly consist of indoor small cells. This new architecture has paved the way for the advent of a new concept called Micro Operator. A micro operator is an entity that provides connections and local 5G services to the customers and relies on local frequency resources. We discuss business models of micro operators in a 5G coopetitive environment and develop a framework to indicate the business model canvas (BMC) of this new concept. Providing BMC for new businesses is a strategic approach to offer value to customers. In this research study, BMC and its elements are introduced and explained for 5G micro operators.