Solvers and scaling

TL;DR

Edge-list analysis is O(E). Independent-pair fitting with binary or cost constraints is usually O(N² × iterations). MENoBiS streams generation and filtering to avoid dense rate matrices.

Large N is memory-feasible

The hard part is usually time, not memory. Public workflows keep multipliers, coordinates, and masks sparse or O(N); generation and filtering stream pair distributions instead of storing dense N x N rate tables.

Practical scaling

Operation	Typical cost	Memory note
Read/write edge list	O(E)	sparse edge table
MENoBiS core statistics	O(E)	single pass
ME strength fit	O(N) to cheap IPF	multiplier arrays
B/W strength fit	O(N² × iterations)	streamed all-pairs sweeps
strength-cost fit	O(N² × iterations)	coordinates are O(N)
strength-edges fit	O(N² × iterations)	zero-inflated
strength-degree fit	O(N² × iterations)	often the slowest common fit
generation	streamed over candidate pairs	output is sparse sampled edges
filtering	O(E) or O(N²) with absent scan	no dense rate matrix

Regimes

Regime	Meaning	Solver behaviour
sparse	degree close to strength; many occupations equal 1	zero-inflated models can be ill-conditioned
dense	moderate support and positive occupations	recommended for tests and benchmarks
saturated	degrees near pair capacity	boundary handling required

Current reliability summary

Case	Status for practical use
ME strength, strength-cost	reliable and fast
ME strength-edges, strength-degree	reliable in dense regimes; sparse can be hard
B strength and cost	reliable with feasible layers
B zero-inflated	generally usable; sparse/saturated regimes need care
W strength	usable; check q<1 diagnostics through fit status
W strength-cost	slower and sensitive at larger N
W zero-inflated	experimental; inspect convergence before scientific use

Memory rules

• Use EdgeTable sparse arrays for observed and sampled networks.
• Do not create dense N x N cost, rate, or probability matrices.
• Use projected coordinates for costs so Rust can compute pair distances on demand.
• Treat absent-edge filtering as an all-pairs scan unless using sparse custom support.

Diagnostics to inspect

Every fit exposes at least:

Field	Meaning
converged	solver reached the requested criterion
status	solver status string
iterations	number of iterations
residual fields	constraint mismatch when available

For exploratory runs, prefer a moderate tolerance such as 1e-6 before asking for stricter recovery.