max_independent_set

std.linalg.max_independent_set · Level L4

The independence number α(G), a maximum independent set (no two of its vertices adjacent), and the number of maximum independent sets, as the maximum cliques of the complement graph.

α(G) = ω(Ḡ)

Signature

max_independent_set(A: f64[n, n]) → f64[], f64[n], f64[]

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 the maximum cliques of the complement in exact rational arithmetic, on all 40 test cases.
All 225 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

max_clique

Called by

min_vertex_cover

sha256:7bfa13e1ea211528265f735b7d22df695610f65577ba2239a71445cb80e0de90

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.max_independent_set · Ω:max_independent_set
Pins: sha256:f9288742b5a246fe51f5aa130f0e01e41a6f10b6f57bfc0cfd7fec130e248b12this graph and the 6 it reaches through calls
Evidence: sha256:fe4ff28915bb3f5bc6ebd80a7dce89359445f4a6755ca5c57e4e31c3eab1e453the 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.