Mathematics · Discrete Mathematics
Minimization Linear-Program Integrality Gap Calculator
Calculate integrality-gap factor from integer-feasible optimum and linear-relaxation lower bound.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=a/b with integer-feasible optimum=126 and linear-relaxation lower bound=105.
- integrality-gap factor=1.2.
Understand Minimization Linear-Program Integrality Gap
One idea, three depths
Choose how deeply to explain Minimization Linear-Program Integrality Gap
Minimization Linear-Program Integrality Gap: Calculate integrality-gap factor from integer-feasible optimum and linear-relaxation lower bound.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Minimization Linear-Program Integrality Gap to answer this question: calculate integrality-gap factor from integer-feasible optimum and linear-relaxation lower bound? Enter integer-feasible optimum and linear-relaxation lower bound; the calculator shows integrality-gap factor. For example: integer-feasible optimum=126 and linear-relaxation lower bound=105 produce integrality-gap factor=1.2. The answer tells you integrality-gap factor.
Age 15Explain it to a 15-year-oldConnect it to the formula
For a minimization problem, the multiplicative integrality gap compares the integer optimum with its linear-relaxation lower bound. This page evaluates the relationship directly. The rule is c=a/b. Its input values are integer-feasible optimum, linear-relaxation lower bound, and the main result is integrality-gap factor. For example: integer-feasible optimum=126 and linear-relaxation lower bound=105 produce integrality-gap factor=1.2.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated minimization linear-program integrality gap relation over the valid real-number domain stated below. The implemented relation is c=a/b, evaluated from integer-feasible optimum, linear-relaxation lower bound to produce integrality-gap factor. For a minimization problem, the multiplicative integrality gap compares the integer optimum with its linear-relaxation lower bound. This page evaluates the relationship directly. State whether the problem is minimization or maximization because the ratio convention reverses.
Inputs and valid domain
- integer-feasible optimum must be a finite real number.
- linear-relaxation lower bound must be a finite real number.
Important boundary: State whether the problem is minimization or maximization because the ratio convention reverses.
The formula
c=a/b
How the calculator works through it
It substitutes integer-feasible optimum, linear-relaxation lower bound into the formula and exposes every numerical step above. The main output is integrality-gap factor.
Read the result correctly
The integrality-gap factor is the direct answer to “calculate integrality-gap factor from integer-feasible optimum and linear-relaxation lower bound.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
integer-feasible optimum=126 and linear-relaxation lower bound=105 produce integrality-gap factor=1.2.
Where this model stops being reliable
State whether the problem is minimization or maximization because the ratio convention reverses.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Minimization Linear-Program Integrality Gap works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Minimization Linear-Program Integrality Gap uses c=a/b. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Sets, membership and finite collections
Sets provide the objects and membership rules that give Minimization Linear-Program Integrality Gap its discrete meaning.
Review this foundation about 6 min
Optional enrichment
- Ordered arrangements
Permutations connect Minimization Linear-Program Integrality Gap to systematic counting and arrangement problems.
Review this foundation about 5 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Read integer-feasible optimum, linear-relaxation lower bound.
- Evaluate the principal relationship: c=a/b.
- Return integrality-gap factor and check the domain conditions described above.
Python
from math import *
def linear_program_integrality_gap_calculator(a, b) -> float:
return (a / b)
assert abs(linear_program_integrality_gap_calculator(126, 105) - 1.2) < 1e-6 * max(1.0, abs(1.2))
C
#include <assert.h>
#include <math.h>
double linear_program_integrality_gap_calculator(double a, double b) {
return (a / b);
}
int main(void) {
const double expected = 1.2;
const double actual = linear_program_integrality_gap_calculator(126, 105);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double linear_program_integrality_gap_calculator(double a, double b) {
return (a / b);
}
int main() {
constexpr double expected = 1.2;
const double actual = linear_program_integrality_gap_calculator(126, 105);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double linear_program_integrality_gap_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global linear_program_integrality_gap_calculator
section .text
linear_program_integrality_gap_calculator:
push rbp
mov rbp, rsp
sub rsp, 32
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-8]
divsd xmm0, [rbp-16]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = linear_program_integrality_gap_calculator(a, b)
result = (a / b);
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := (a / b);
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Minimization Linear-Program Integrality Gap Calculator. MW SysArc Tools. https://math.mwsysarc.com/discrete-mathematics/linear-program-integrality-gap-calculator
MLA 9
MW SysArc. “Minimization Linear-Program Integrality Gap Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/discrete-mathematics/linear-program-integrality-gap-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Minimization Linear-Program Integrality Gap Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/discrete-mathematics/linear-program-integrality-gap-calculator.
Harvard
MW SysArc (2026) ‘Minimization Linear-Program Integrality Gap Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/discrete-mathematics/linear-program-integrality-gap-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_linear_program_integrality_gap_calculator_2026,
author = {{MW SysArc}},
title = {Minimization Linear-Program Integrality Gap Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/discrete-mathematics/linear-program-integrality-gap-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Minimization Linear-Program Integrality Gap Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/discrete-mathematics/linear-program-integrality-gap-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Minimization Linear-Program Integrality Gap do?
Calculate integrality-gap factor from integer-feasible optimum and linear-relaxation lower bound.
How does the Minimization Linear-Program Integrality Gap work?
The calculator applies c=a/b. For a minimization problem, the multiplicative integrality gap compares the integer optimum with its linear-relaxation lower bound. This page evaluates the relationship directly.
What can I learn from the Minimization Linear-Program Integrality Gap?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .