Reason for the differing search times under two assumptions

Determine why the backtracking search and Boolean SAT-solver search have substantially different running times for the “Our neighbors are neighbors” and “Our neighbors aren’t neighbors” assumptions in attempted constructions of a strongly regular graph with parameters (99,14,1,2).

Background

The paper reports that both neighbor assumptions are ruled out computationally, but the computational methods behave differently. The simple backtracking algorithm is effective for one assumption but takes too long for the other, which requires a more complicated SAT-based search. The reason for this discrepancy is explicitly left unresolved.

References

Interestingly, the simple backtracking search algorithm from the Our neighbors are neighbors'' section did not work on theOur neighbors are neighbors'' assumption (it took too long - it may have worked eventually if given enough computing time). A more complicated search involving a boolean SAT solver was used. It is unclear why the two assumptions would have such different search times.

— An Induced Subgraph Paradigm for Strongly Regular Graph Constructions  (2610.22299 - Baker, 15 Oct 2026) in Section 5, subsection “Our neighbors aren't neighbors” assumption (impossible)