Topology · x
X Graph
All n nodes point to a hub, which fans out to k leaf nodes.
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 · edges16 · 15
Closure |TC|65
Closure / edges4.3×
A small instance from the generator the benchmark runs with n from 100 upwards.
Definition
Symbol
X_{n,k}
Edges
\{(i, n+1) \mid i \in 1..n\} \cup \{(n+1, n+1+j) \mid j \in 1..k\}
Generator
engine.data_generator.DataGenerator.generate_x_graphgenerate_db.py
def generate_x_graph(self, n: int) -> Generator[tuple[int, int], None, None]:
"""Generate a X graph with n nodes."""
logging.info(f'Generating X graph for n={n}')
for i in range(1, n + 1):
yield (i, n + 1)
for j in range(1, self.k + 1):
yield (n + 1, n + 1 + j)