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The CAP theorem states that only two of these properties can be simultaneously guaranteed in a distributed service: (i) consistency, (ii) availability, and (iii) network partition tolerance. This theorem was stated and proved assuming that "consistency" refers to atomic consistency. However, multiple consistency models exist and atomic consistency is located at the strongest edge of that spectrum.Many distributed services deployed in cloud platforms should be highly available and scalable. Network partitions may arise in those deployments and should be tolerated. One way of dealing with CAP constraints consists in relaxing consistency. Therefore, it is interesting to explore the set of consistency models not supported in an available and partition-tolerant service (CAP-constrained models). Other weaker consistency models could be maintained when scalable services are deployed in partitionable systems (CAP-free models). Three contributions arise: (1) multiple other CAPconstrained models are identified, (2) a borderline between CAP-constrained and CAP-free models is set, and (3) a hierarchy of consistency models depending on their strength and convergence is built.

Elasticity is a goal of cloud computing. An elastic system should manage in an autonomic way its resources, being adaptive to dynamic workloads, allocating additional resources when workload is increased and deallocating resources when workload decreases. PaaS providers should manage resources of customer applications with the aim of converting those applications into elastic services. This survey identifies the requirements that such management imposes on a PaaS provider: autonomy, scalability, adaptivity, SLA awareness, composability and upgradeability. This document delves into the variety of mechanisms that have been proposed to deal with all those requirements. Although there are multiple approaches to address those concerns, providers' main goal is maximisation of profits. This compels providers to look for balancing two opposed goals: maximising quality of service and minimising costs. Because of this, there are still several aspects that deserve additional research for finding optimal adaptability strategies. Those open issues are also discussed.