Testing of sequences by simulation

Let ξ be a random integer vector, having uniform distribution P{ξ = (i1, i2, . . . , in) = 1/n} for 1 ≤ i1, i2, . . . , in ≤ n. A realization (i1, i2, . . . , in) of ξ is called good, if its elements are different. We present algorithms Backward, Forward, Linear, Random, Tree, Garbage, Bucket which decide whether a given realization is good. We analyse the running time of these algorithms using simulation gathering data on all possible inputs for small values of n and generating random inputs for large values of n [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. The research is supported by the project TÁMOP-4.2.1.B-09/1/KMR-2010-0003 of Eötvös Loránd University.