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In a cloud marketplace, the existence of wide range of Cloud Service Providers (CSPs) makes it hard for the Cloud Users (CUs) to find an appropriate CSP based on their requirements. The design of a suitable service selection framework helps the users in the selection of a suitable CSP, while motivating the CSPs to satisfy the assured Service Level Agreement (SLA) and enhance the Quality of Service (QoS). Existing service selection models employ random assignment of weights to the QoS attributes, replacement of missing data by random values, etc. which results in an inaccurate ranking of the CSPs. Moreover, these models have high computational overhead. In this study, a novel cloud service selection architecture, Hypergraph based Computational Model (HGCM) and Minimum Distance-Helly Property (MDHP) algorithm have been proposed for ranking the cloud service providers. Helly property of the …