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Consider a system consisting of a set ofn processes, P~, P2 . . . . . Pn, and a set of serially reusable resources of m different types, R1, R~ . . . . . R,~. It is assumed that the system is "claim-limited," that is, its "claim matrix" C, whose (i, j ) element C(i, j) is the maximum number of units of R: that may be needed by P, at the same time, is known a priori. It is desired to design a deadlock-free system, that is, one which never deadlocks for any allocation sequence within the limits given by C. For j ffi 1, 2 . . . . . m, let a, (>0) be the cost of one unit of Rj. An algorithm for designing a deadlock-free system with the minimum resource cost is presented. Its running time is bounded by O(ca(m) + mlogm), where e ts the number of nonzero elements in C and a, is the inverse of Ackermann's function, which is very slowly growing

Design of Minimum-Cost Deadlock-Free Systems