Algorithm Min‑Link(G_c = (V, E)):
Input: Canonical graph G_c
Output: Minimal‑link graph G_min = (V, E_min)
1 C ← (u,v,l) ∈ E
2 A ← E \ C // Acyclic candidate set
3 G_A ← (V, A)
4 // ---- Pass 1: Transitive reduction on DAG ----
5 if not is_DAG(G_A):
6 A ← remove_feedback_edges(G_A) // fallback, rarely needed
7 R ← transitive_reduction(G_A) // O(|V|·|E|) using BFS per node
8 // ---- Pass 2: Preserve feedback cycles ----
9 E_min ← R ∪ C
10 // ---- Pass 3: Local pruning within cycles ----
11 for each (u,v,l) ∈ C:
12 if exists alternative path p from u to v in G_min \ (u,v,l):
13 E_min ← E_min \ (u,v,l) // safe removal
14 return (V, E_min)
Complexity:
Thus the total runtime is O(|V|·|E|), comfortably scaling to graphs with >10⁶ edges on commodity hardware (see Section 5).
| Metric |
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Large‑scale engineering projects involve many subsystem models (mechanical, electrical, control, software) that are authored in different tools (CAD, Simulink, Modelica, SysML) and stored using a variety of data exchange formats (XML, JSON, HDF5). When these models are integrated into a digital twin or a system‑level simulation, a common representation is required. Algorithm Min‑Link(G_c = (V, E)): Input: Canonical graph
Two practical challenges dominate today’s integration workflow:
| Challenge | Existing Solutions | Limitations | |-----------|-------------------|-------------| | Heterogeneous versioning (e.g., 02‑10‑21 vs. 2021‑02‑10) | Manual scripts, ad‑hoc parsers | Error‑prone, poor scalability | | Excessive inter‑connection density (hundreds of thousands of links) | Direct import, pruning by hand | Undermines simulation speed, inflates memory use |
Our contribution is a three‑stage pipeline that (i) homogenizes versioned subsystem data, (ii) converts it into a uniform graph model, and (iii) optimally reduces the link set while preserving functional semantics.
The rest of the paper is organized as follows. Section 2 surveys related work. Section 3 formalizes the problem and introduces the pipeline architecture. Section 4 details the Min‑Link algorithm. Section 5 describes the experimental setup and results. Section 6 discusses limitations and future directions. Finally, Section 7 concludes. Complexity:
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