Topology · path
Path Graph
A simple directed path 1→2→3→...→n. TC is a dense upper-triangular graph.
Evaluation
Linear · T ∘ E–iterations (left / right recursion)
Doubling · T ∘ T–iterations (double recursion)
iteration 1new pairs per iteration
Point at a node (or tab to the drawing and use the arrow keys) to see every node it reaches, wave by wave. Those pairs are its rows of the closure.
Nodes · edges7 · 6
Closure |TC|21
Closure / edges3.5×
A small instance from the generator the benchmark runs with n from 100 upwards.
Definition
Symbol
P_n
Edges
\{(i,i+1) \mid i \in 1..n-1\}
Generator
engine.data_generator.DataGenerator.generate_path_graphgenerate_db.py
def generate_path_graph(self, n: int) -> Generator[tuple[int, int], None, None]:
"""Generate a path graph with n nodes."""
logging.info(f'Generating path graph for n={n}')
for i in range(1, n):
yield (i, i + 1)