Context-Aware Computing

Suppose that when the probability of e changes from $p_j^{\text{'}}\left(e\right)\text{to}{p}_{j+1}^{\text{'}}\left(e\right),$ the positions of result tuple x and y are inverted (in $R_j^{\text{'}},$ x is ranked before y; in $R_{j+1}^{\text{'}}$ x is ranked after y). If we use x0 and xj to denote the position of x in R0 and $R_j^{\text{'}},$ respectively, and y0 and yj the position of y in R0 and $R_j^{\text{'}},$ respectively, then

$\begin{array}{l}{\text{Distance}}^w\left(R_{j+1}^{\text{'}},Top{K}_0\right)={\text{Distance}}^w\left(R_j^{\text{'}},Top{K}_0\right)+\backslash \\ \{\begin{array}{cc}2w_{x_j}& \text{if}{\text{x}}_0\le x_j\text{and}{\text{y}}_0\ge y_j;\\ -2w_{x_j}& \text{if}{\text{x}}_0>x_j\text{and}{\text{y}}_0\ge y_j;\\ 0& \text{if}\left({\text{x}}_0>x_j\text{and}{\text{y}}_0\ge y_j\right)or\left({\text{x}}_0\le x_j\text{and}{\text{y}}_0\ge y_j\right).\end{array}\left(11.22\right)\end{array}$

Hence, all the distances ${\text{Distance}}^{}$