# Image:ReactionNets-structure-mis-n04-01-nets.png

Undirected graph given

Chemical reaction network $A=\langle \mathcal{M},\mathcal{R}\rangle$ designed to solve the maximal independent set problem, given an undirected graph. The detail algorithm can be found in BioSysBio Abstract, Appendix B.

The set $\mathcal{M}$ of molecular species consists of eight species:

$\mathcal{M}=\{s_1^0, s_1^1, s_2^0, s_2^1, s_3^0, s_3^1, s_4^0, s_4^1\}$.

(Note: species $s_1^0$ is denoted as $\mathsf{s10}$ in the figure.)

The set $\mathcal{R}$ of reaction rules is composed of three sets:

$\mathcal{R} = (\mathcal{V} \cup \mathcal{N} \cup \mathcal{D})$

where

$\mathcal{V}=\bigcup_{i=1}^4\mathcal{V}^i$, $\mathcal{N}=\bigcup_{i=1}^4\mathcal{N}^i$, and $\mathcal{D}=\bigcup_{i=1}^4\mathcal{D}^i$.

Specifically,

$\begin{matrix} \mathcal{V}=\{&\underbrace{s_2^0 + s_3^0 \rightarrow 2 s_1^1},& \underbrace{s_1^0 + s_3^0 \rightarrow 2 s_2^1},& \underbrace{s_1^0+s_2^0+s_4^0 \rightarrow 3s_3^1},& \underbrace{s_3^0\rightarrow s_4^1}&\}\\ &\mathcal{V}_1&\mathcal{V}_2&\mathcal{V}_3&\mathcal{V}_4&\\ \end{matrix}$,

$\begin{matrix} \mathcal{N}=\{&\underbrace{s_2^1 \rightarrow s_1^0, s_3^1 \rightarrow s_1^0},& \underbrace{s_1^1 \rightarrow s_2^0, s_3^1 \rightarrow s_2^0}&, \underbrace{s_1^1 \rightarrow s_3^0, s_2^1 \rightarrow s_3^0, s_4^1 \rightarrow s_3^0},& \underbrace{s_3^1\rightarrow s_4^0}&\}\\ &\mathcal{N}_1&\mathcal{N}_2&\mathcal{N}_3&\mathcal{N}_4&\\ \end{matrix}$,

and

$\begin{matrix} \mathcal{D}=\{&\underbrace{s_1^0 + s_1^1 \rightarrow \emptyset}, & \underbrace{s_2^0 + s_2^1 \rightarrow \emptyset}, & \underbrace{s_3^0 + s_3^1 \rightarrow \emptyset}, & \underbrace{s_4^0 + s_4^1 \rightarrow \emptyset}&\}\\ &\mathcal{D}_1&\mathcal{D}_2&\mathcal{D}_3&\mathcal{D}_4&\\ \end{matrix}$.

## File history

Click on a date/time to view the file as it appeared at that time.

 Date/Time Dimensions User Comment current 06:56, 27 September 2006 600×400 (8 KB) NaokiMatsumaru (Talk | contribs) (Chemical reaction network to solve a maximal independent set problem. The undirected graph given consists of four vertexes and four edges. )

The following 3 pages link to this file: