A deadlock avoidance technique, based on a method of representing directed acyclic graphs, is presented. This technique is suitable for systems with single resources of each resource type. The deadlock avoidance problem considered is the problem of changing a directed acyclic graph while keeping it acyclic. The resource allocation algorithm involves three operations on edges corresponding to release of a resource from a process, unsuccessful allocation of a resource to a process, and successful allocation of a resource to a process, where the allocations include a previous detection of cycles. A path matrix representation is used, making it possible to detect cycles efficiently. The low cost of cycle detection can amortize the cost of the other operations and linear (or even constant) amortized time for one operation can be attained in dense systems.>