Algorithm 1 SE-KIA (offline component)

1:Input: Query logs $\mathcal{Q}$, search corpus $\mathcal{C}$, co-occurrence threshold $\tau =10$, search method Search(keywords, $\mathcal{C}$) that returns an ordered list of documents ranked by relevance   2:Output: Keyword co-occurrence word graph $G=(V,E)$   3:Step 1: Data Extraction   4:Parse $\mathcal{Q}$ to extract all queries containing exactly two keywords   5:Filter out pairs with frequency $f(A,B)>=\tau$, obtaining set $\mathcal{P}=\left\{\right(A,B\left)\right\}$   6:Step 2: Posteriori Search Result Retrieval   7:for each $(A,B)\in \mathcal{P}$ do   8:   $Y\leftarrow \mathrm{Search}(A\&B,\mathcal{C})$   9:   $Y_A\leftarrow \mathrm{Search}(A,\mathcal{C})$ 10:   $Y_B\leftarrow \mathrm{Search}(B,\mathcal{C})$ 11:end for 12:Step 3: Semantic Entropy Calculation 13:for each $(A,B)\in \mathcal{P}$ do 14:   Compute intersections: 15:   $Y\cap Y_A=\{Z_{A1},Z_{A2},\dots ,Z_{An}\}$ 16:   $Y\cap Y_B=\{Z_{B1},Z_{B2},\dots ,Z_{Bm}\}$ 17:   Calculate occurrence counts: 18:   $t_A\left(z\right)\leftarrow$ number of documents $z\in Z_A$ in $Y_A$ 19:   $t_B\left(z\right)\leftarrow$ number of documents $z\in Z_B$ in $Y_B$ 20:   Compute associated probabilities: 21:   $p_{Y_A|Y}\left(z\right)={\displaystyle \frac{t_A\left(z\right)}{{\sum }_{z\in Z_A}{t}_A\left(z\right)}}$ 22:   $p_{Y_B|Y}\left(z\right)={\displaystyle \frac{t_B\left(z\right)}{{\sum }_{z\in Z_B}{t}_B\left(z\right)}}$ 23:   Compute semantic entropy: 24:   $S(Y_A,Y)=-{\sum }_{z\in Z_A}{p}_{Y_A|Y}\left(z\right)log{p}_{Y_A|Y}\left(z\right)$ 25:   $S(Y_B,Y)=-{\sum }_{z\in Z_B}{p}_{Y_B|Y}\left(z\right)log{p}_{Y_B|Y}\left(z\right)$ 26:end for 27:Step 4: Relative importance determination 28:for each $(A,B)\in \mathcal{P}$ do 29:   if $S(Y_A,Y)<S(Y_B,Y)$ then 30:      $w_{AB}\leftarrow 1$ 31:    else if $S(Y_A,Y)>S(Y_B,Y)$ then 32:      $w_{AB}\leftarrow -1$ 33:   else 34:      $w_{AB}\leftarrow 0$ 35:   end if 36:end for 37:Step 5: Graph Construction 38:Initialize $G=(V,E)$ where $V\leftarrow \varnothing$, $E\leftarrow \varnothing$ 39:for each $(A,B)\in \mathcal{P}$ do 40:   $V\leftarrow V\cup \{A,B\}$ 41:   $E\leftarrow E\cup \left\{(A,B,w_{AB})\right\}$ 42:end for 43:return $G=(V,E)$