This paper discusses the generalized mutual exclusion problem defined by H. Kakugawa and M. Yamashita. A set of processes shares a set of resources of an identical type. Each resource must be accessed by at most one process at any time. Each process may have different accessible resources. If two processes have no common accessible resource, it is reasonable to ensure a condition in resource allocation, which is called allocation independence in this paper, i. e. , resource allocation to those processes must be performed without any interference. In this paper, we define a new structure, sharing structure coterie. By using a sharing structure coterie, the resource allocation algorithm proposed by H. Kakugawa and M. Yamashita ensures the above condition. We show a necessary and sufficient condition of the existence of a sharing structure coterie. The decision of the existence of a sharing structure coterie for an arbitrary distributed system is NP-complete. Furthermore, we show a resource allocation algorithm which guarantees the above requirement for distributed systems whose sharing structure coteries do not exist or are difficult to obtain.

In this paper, parallelization methods for quantum circuits are studied, where parallelization of quantum circuits means to reconstruct a given quantum circuit to one which realizes the same quantum computation with a smaller depth, and it is based on using additional bits, called ancillae, each of which is initialized to be in a certain state. We propose parallelization methods in terms of the number of available ancillae, for three types of quantum circuits. The proposed parallelization methods are more general than previous one in the sense that the methods are applicable when the number of available ancillae is fixed arbitrarily. As consequences, for the three types of n-bit quantum circuits, we show new upper bounds of the number of ancillae for parallelizing to logarithmic depth, which are 1/log n of previous upper bounds.