Derailleur gears several standards in use, and in each the product of the derailleur's actuation ratio and the length of cable pulled must equal the pitch of the rear sprockets. The following standards exist. Some rear derailleurs, especially for mountain bikes, incorporate a clutch to keep the lower length of chain in sufficient tension to prevent the chain from striking the bottom of the chain stay, called "chain slap", and which can damage the chain stay. Clutches are also helpful in preventing the chain from derailing from the chain ring on systems without a front derailleur. The front derailleur only has to
Library sort sort it is based on, library sort is a stable comparison sort and can be run as an online algorithm; however, it was shown to have a high probability of running in O(n log n) time (comparable to quicksort), rather than an insertion sort's O(n). The mechanism used for this improvement is very similar to that of a skip list. There is no full implementation given in the paper, nor the exact algorithms of important parts, such as insertion and rebalancing. Further information would be needed to discuss how the efficiency of library sort compares to that of other sorting