Combinatorial and Discrete Algorithms

This group gathers numerical algorithms that operate on discrete, symbolic or combinatorial structures rather than continuous quantities, including polynomial algorithms such as polynomial long division, factorization of polynomials and Grobner basis methods, bit-manipulation tricks such as the XOR swap algorithm and bit-reversal permutation, tree and sequence construction algorithms such as the Garsia-Wachs algorithm, calendrical calculations such as the Doomsday rule, the date of Easter and determination of the day of the week, hardware memory-test algorithms such as the march algorithm, and estimation heuristics such as the Manhattan address algorithm. Their shared work is manipulating exact discrete or symbolic structures, as distinct from an approximate numeric computation over real numbers, which belongs to one of the other groups.