and "weak" references for child-to-parent relationships. Systems may also be designed to tolerate or correct the cycles they create in some way. Developers may design code to explicitly "tear down" the references in a data structure when it is no longer needed, though this has the cost of requiring them to manually track that data structure's lifetime. This technique can be automated by creating an "owner" object that does the tearing-down when it is destroyed; for instance, a Graph object's destructor could delete the edges of its GraphNodes, breaking the reference cycles in the graph. Cycles may even be ignored in systems with short lives and a small amount of cyclic garbage, particularly when the system was developed using a methodology of avoiding cyclic data structures wherever possible, typically at the expense of efficiency. Computer scientists have also discovered ways to detect and collect reference cycles automatically, without requiring changes in the data structure design. One simple solution is to periodically use a tracing garbage collector to reclaim cycles; since cycles typically constitute a relatively small amount of reclaimed space, the collector can be run much less often than with an ordinary tracing garbage collector. Bacon describes a cycle-collection algorithm for reference counting with similarities to tracing collectors, including the same theoretical time bounds. It is based on the observation that a cycle can only be isolated when a reference count is decremented to a nonzero value. All objects which this occurs on are put on a roots list, and then periodically the program searches through the objects reachable from the roots for cycles. It knows it has found a cycle that can be collected when decrementing all the reference counts on a cycle of references brings them all down to zero. An enhanced version of this algorithm by Paz et al. is able to run concurrently with other operations and improve its efficiency by using the update coalescing method of Levanoni and Petrank. Variant forms Although it is possible to augment simple reference counts in a variety of ways, often a better solution can be found by performing reference counting in a fundamentally different way. Here we describe some of the variants on reference counting and their benefits and drawbacks. Weighted reference counting In weighted reference counting, each reference is assigned a weight, and each object tracks not the number of references referring to it, but the total weight