Hyperreconfigurable architectures adapt their reconfiguration abilities during run time in order to achieve fast dynamic reconfiguration. Models for such architectures have been proposed that change their ability for reconfiguration during hyperreconfiguration steps and in ordinary reconfiguration steps reconfigure the actual contexts for a computation within the limits that have been set by the last hyperreconfiguration step. In this paper we study algorithmic aspects of how to optimally decide what hyperreconfiguration steps should be done during a computation in order to minimize the total time necessary for hyperreconfiguration and ordinary reconfiguration. It is shown that the general problem is NP-hard but fast polynomial time algorithms are given to solve this problem on different types of hyperreconfigurable architectures. These include newly introduced architectures that use a cache to store hypercontexts. We define an example hyperreconfigurable architecture and illustrate the introduced concepts for three application problems.
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