residual_bfs

std.linalg.residual_bfs · Level L2

Breadth-first search from vertex 0 along the edges with positive residual capacity R: which vertices are reached, and each one's parent on a shortest path. A Scan of bfs_step, n layers.

BFS from 0 on {(u, v) : R(u, v) > 0}

Signature

residual_bfs(R: f64[n, n]) → f64[n], f64[n]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Equal to the reference layer by layer from vertex 0, the smallest parent first in exact rational arithmetic, on all 40 test cases.
All 340 float64 results are exact: the error is zero.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them exact, with zero error.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 100%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 0

Identity

Calls

bfs_step

Called by

augment augmentable max_flow

sha256:697ba7324eacda970b3c0091d4052005bbcbd35d197ae78f396f4a19281992cc

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.linalg.residual_bfs · Ω:residual_bfs
Pins: sha256:5bea10ae5f249d7c4a8899304ccf2d99947a2191b6f8844a1a9475e207be969dthis graph and the 1 it reaches through calls
Evidence: sha256:b2eccc682e2e931a6ccfab90c901527e60b06e7cae25ac83b7484afd7fcad48athe hash of its verification record
Needs: no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.