Papers^γ

How to efficiently generate combinatorial structures such as posets, trees, B-trees, graphs, permutations, set partitions, Dyck paths, multisets or necklaces ... ? The Ruskey's book gives answers. It contains many surprising descriptions (and bibliographic references) of constant amortized time (CAT) and loopless algorithms. 　 > **CAT Algorithms** The holy grail of generating combinatorial objects is to find an algorithm that runs in Constant Amortized Time. This means that the amount of computation, after a small amount of preprocessing, is proportional to the number of objects that are listed. We do not count the time to actually output or process the objects; we are only concerned with the amount of data structure change that occurs as the objects are being generated. 　　　　_ Ruskey's book, page 8 _ 　 > ** Loopless algorithm ** is an imperative algorithm that generates successive combinatorial objects, such as partitions, permutations, and combinations, in constant time and the first object in linear time 　　　　_ https://en.wikipedia.org/wiki/Loopless_algorithm _