Complexity Formalization for Semantification of Workflows[edit]
Let G = (V, E) be a knowledge graph where V is the set of nodes (vertices) and E is the set of edges.
Complexity Measure[edit]
We define the complexity C of a workflow as:
[math]C = \alpha \cdot |V| + \beta \cdot |E| + \gamma \cdot d + \delta \cdot b + \frac{\epsilon \cdot T_c}{T_b}[/math]
Where:
|V| is the number of nodes
|E| is the number of edges
d is the depth of the graph structure
b is the breadth of the graph structure
T_c is the transaction cost
T_b is the transaction benefit
α, β, γ, δ, and ε are weighting factors
\section{Complexity Formalization for Semantification of Workflows}
Let $G = (V, E)$ be a knowledge graph where $V$ is the set of nodes (vertices) and $E$ is the set of edges.
\subsection{Complexity Measure}
We define the complexity $C$ of a workflow as:
\begin{equation}
C = \alpha \cdot |V| + \beta \cdot |E| + \gamma \cdot d + \delta \cdot b + \frac{\epsilon \cdot T_c}{T_b}
\end{equation}
Where:
\begin{itemize}
\item $|V|$ is the number of nodes
\item $|E|$ is the number of edges
\item $d$ is the depth of the graph structure
\item $b$ is the breadth of the graph structure
\item $T_c$ is the transaction cost
\item $T_b$ is the transaction benefit
\item $\alpha, \beta, \gamma, \delta,$ and $\epsilon$ are weighting factors
\end{itemize}
\subsection{Interpretation}
\begin{itemize}
\item The first four terms ($|V|, |E|, d, b$) represent the structural complexity of the workflow.
\item The last term ($T_c / T_b$) represents the efficiency of the workflow.
\item Lower values of $C$ indicate simpler, more efficient workflows.
\item Higher values of $C$ indicate more complex, potentially less efficient workflows.
\end{itemize}
\subsection{Example: Ice Cream Purchase}
Consider a simple ice cream purchase scenario:
\begin{itemize}
\item $|V| = 2$ (customer, vendor)
\item $|E| = 1$ (transaction)
\item $d = 1$ (single-level interaction)
\item $b = 2$ (two parties involved)
\item $T_c$ is low (short distance, no waiting, kind interaction)
\item $T_b$ is high (tasty ice cream on a hot day)
\end{itemize}
This scenario would result in a low complexity value $C$, indicating a simple and efficient workflow.
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Interpretation[edit]
The first four terms (|V|, |E|, d, b) represent the structural complexity of the workflow.
The last term (T_c / T_b) represents the efficiency of the workflow.
Lower values of C indicate simpler, more efficient workflows.
Higher values of C indicate more complex, potentially less efficient workflows.
Example: Ice Cream Purchase[edit]
Consider a simple ice cream purchase scenario:
|V| = 2 (customer, vendor)
|E| = 1 (transaction)
d = 1 (single-level interaction)
b = 2 (two parties involved)
T_c is low (short distance, no waiting, kind interaction)
T_b is high (tasty ice cream on a hot day)
This scenario would result in a low complexity value C, indicating a simple and efficient workflow.