Algorithm 1$SubTSSH(H=(V,E),t_V,t_E)$

1:$S=\varnothing$ 2:while$V\ne \varnothing$do 3:    if $\exists u\in V|t_V\left(u\right)=0$ then        ▹ Case 1.a: if a node exists with threshold 0, it is self-influenced 4:        $V=V-\left\{u\right\}$;         ▹ Remove u from the hypergraph 5:        $UpdateThresholds(H,u)$;         ▹ Reduce the thresholds of the edges containing u 6:        $UpdateSizes(H,u)$;         ▹ Reduce the size of the edges containing u 7:    else 8:        if $\exists e\in E|t_E\left(e\right)=0$ then        ▹ Case 1.b: if an edge exists with threshold 0, it is self-influenced 9:           $E=E-\left\{e\right\}$;         ▹ Remove e from the hypergraph 10:           $UpdateThresholds(H,e)$;         ▹ Reduce the thresholds of the nodes belonging to e 11:           $UpdateDegrees(H,e)$;         ▹ Reduce the degree of the nodes belonging to e 12:        else 13:           if $\exists u\in U|\delta \left(u\right)<t_V\left(u\right)$ then        ▹ Case 2: v cannot be influenced by its neighbors 14:               $S=S\cup \left\{u\right\}$;         ▹ Add u to the seed set S 15:               $V=V-\left\{u\right\}$;         ▹ Remove u from the hypergraph 16:               $UpdateThresholds(H,u)$;         ▹ Reduce the thresholds of the edges containing u 17:               $UpdateSizes(H,u)$;         ▹ Reduce the size of the edges containing u 18:           else        ▹ Remove a node v or an edge e 19:               $u=argmi{n}_{v\in V}\frac{t_V\left(v\right)}{\delta \left(v\right)\left(\delta \right(v)+1)}$         ▹$\delta \left(v\right)$ is the current degree of the node v 20:               $e=argmi{n}_{he\in E}\frac{t_E\left(he\right)}{\lambda \left(he\right)\left(\lambda \right(he)+1)}$        ▹$\lambda \left(he\right)$ is the current size of the edge $he$ 21:               if $\frac{t_V\left(u\right)}{\delta \left(u\right)\left(\delta \right(u)+1)}<\frac{t_E\left(e\right)}{\lambda \left(e\right)\left(\lambda \right(e)+1)}$ then        ▹ Case 3.a: Remove u 22:                   $V=V-\left\{u\right\}$;         ▹ Remove u from the hypergraph 23:                   $UpdateSizes(H,u)$;         ▹ Reduce the size of the edges containing u 24:               else        ▹ Case 3.b: Remove e 25:                   $E=E-\left\{e\right\}$;         ▹ Remove e from the hypergraph 26:                   $UpdateDegrees(H,e)$;         ▹ Reduce the degree of the nodes belonging to e 27:return S