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Performance Analysis of Fisher-Yates and HEK Shuffle Algorithms

For the analysis of the two algorithms, a non-random sequence adapted for the "Runs Test" consisting of 200000 data points was used. Both sequences consist of 2, 4, and 8 Runs, and each Run is placed sequentially. The initial patterns of the sequences are as follows:

Let N represent the length of the array.

Runs 2: {0..0(N/2),1..1(N/2)}
Runs 4: {0..0(N/4),1..1(N/4),....,0..0(N/4),1..1(N/4)}
Runs 8: {0..0(N/8),1..1(N/8),....,0..0(N/8),1..1(N/8)}

The "Runs Test" was used for randomness analysis, and the "Mann-Whitney U Test" was used to compare performance data. The graphs related to the results are provided below:

Fisher-Yates ve HEK Karıştırma Algoritmalarının Performans Analizi

İki algoritmanın analizi için 200000 veriden oluşan "Runs Test" için uyarlanmış rastgele olmayan dizi kullanılmıştır. İki dizi de 2, 4 ve 8 Runs'tan oluşmakta ve her iki Run ardışık olarak yerleştirilmektedir. Dizilerin başlangıç desenleri aşağıdadır:

N dizinin eleman sayısını göstermek üzere.

Runs 2: {0..0(N/2),1..1(N/2)}
Runs 4: {0..0(N/4),1..1(N/4),....,0..0(N/4),1..1(N/4)}
Runs 8: {0..0(N/8),1..1(N/8),....,0..0(N/8),1..1(N/8)}

şeklindedir. Rastgelelik analizi için "Runs Test" ve performans verilerinin karşılaştırılması için "Mann-Whitney U Test" kullanılmıştır. Aşağıda sonuçlarla ilgili grafikler verilmiştir:

Runs 2, R=0.5

FYHEK2

Runs 4, R=0.25

FYHEK4

Runs 8, R=0.125

FYHEK8

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