A Fast Algorithm for Finding Strong Starters
Jeffrey H. Dinitz, Douglas R. Stinson · SIAM Journal on Algebraic and Discrete Methods · 1981
A strong starter (of order n) in an additive Abelian group G of odd order $n = 2t + 1$ is a set $S = \{ \{ x_1 ,y_1 \}, \{ x_2 ,y_2 \}, \cdots , \{ x_t ,y_t \} \}$ which satisfies the following properties: (i) $\{ x_1 ,x_2 , \cdots ,x_t ,y_{1}, y_2 , \cdots ,y_t \} = G\backslash \{ 0 \}$, (ii) $\{ \pm (y_1 - x_i ) | \{ x_i ,y_i \} \in S \} = G\backslash \{ 0 \}$, (iii) $x_i + y_i e x_j + y_{i}$ if $i e j$, and $x_i + y_i e 0$, for any i. We present a fast algorithm for finding strong starters in Abelian groups.