Use spatial costs

TL;DR

Strength-cost models match strengths and total expected cost. Public MENoBiS APIs use projected XY coordinates and compute Euclidean pair costs on demand; do not materialize dense N x N cost matrices.

When to use strength-cost

Use it when distance, travel time proxy, or spatial separation is an explicit structural constraint. It is common for urban mobility and other origin-destination networks.

Other metrics are possible

Euclidean distance is the public built-in provider. Road distance, travel time, or other metrics can be added by implementing a Rust cost provider that computes one pair cost at a time. See Extending thesis cases.

Do not use latitude/longitude degrees directly. Project first, then pass planar x and y.

Constraint

For projected coordinates, MENoBiS uses:

\[d_{ij}=\sqrt{(x_i-x_j)^2+(y_i-y_j)^2}\]

and fits:

\[C=\sum_{ij}\mathbb{E}[t_{ij}]d_{ij}.\]

Python example

from menobis.models import Constraint, ModelFamily, fit_model, sample_model

fit = fit_model(
    family=ModelFamily.ME,
    constraint=Constraint.STRENGTH_COST,
    strength_out=strength_out,
    strength_in=strength_in,
    target_cost=total_cost,
    coord_x=x,
    coord_y=y,
    self_loops=False,
)

sample = sample_model(
    family=ModelFamily.ME,
    constraint=Constraint.STRENGTH_COST,
    fit=fit,
    coord_x=x,
    coord_y=y,
    seed=42,
)

Scaling warning

Item	Guidance
Coordinate storage	O(N)
Fitting sweeps	usually O(N² × iterations)
Generation/filtering	streamed over candidate pairs
Dense cost matrix	not part of public API

See Solvers and scaling before running large strength-cost fits.