The current document is directed a resource-exchange system that facilitates resource exchange and sharing among computing facilities. The currently disclosed methods and systems employ efficient, distributed-search-based auction methods and subsystems within distributed computer systems that include large numbers of geographically distributed data centers to locate resource-provider computing facilities that match the resource needs of resource-consumer computing facilities. Multiple security methods and subsystems are employed to prevent unauthorized access to resource-exchange-system services, to secure resource-exchange-system-participant data from unauthorized access, and to prevent hosted virtual machines and other hosted computational entities from interfering with operation of native virtual machines and other native computational entities within hosting resource-provider computing facilities.