Description
Generate a nonempty finite subset family and positive costs with a planted cover witness; feasible selections may cover elements multiple times, duplicate columns allowed, with no minimum-cost claim.
An optimization instance defines choices, constraints, and an objective. A feasible witness demonstrates that its stated constraints can be met; it establishes optimality only when the tool actually computes and verifies an optimum.
Generate a nonempty finite subset family and positive costs with a planted cover witness; feasible selections may cover elements multiple times, duplicate columns allowed, with no minimum-cost claim.
When to use this tool
Use this generator to create reproducible set covering instance cases from the supplied model or bank. Inspect the returned evidence before using cases in a test or exercise.
How to use the tool and how it works
- Supply universeSize, setCount, plantedSetCount, extraInclusionProbability, minimumCost, maximumCost in the field shapes below. Set seed when you need an explicit replay.
- Run the tool and correct any input error. For generated controls, distinguish a successful fixture containing an invalid case from failure to generate the fixture.
- Read universe, subsets, costs, witnessIndices, witnessCost. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.
Construct a family with a planted partition that also supplies a covering witness, then add sampled subsets and integer costs. Return the planted indexes and exact total witness cost with the full universe and family.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| universeSize | Universe Size | Required. Safe integer; minimum 1; maximum 64. |
| setCount | Set Count | Required. Safe integer; minimum 1; maximum 128. |
| plantedSetCount | Planted Set Count | Required. Safe integer; minimum 1; maximum 64. |
| extraInclusionProbability | Extra Inclusion Probability | Required. Finite number; minimum 0; maximum 1. |
| minimumCost | Minimum Cost | Required. Safe integer; minimum 1; maximum 9007199254740991. |
| maximumCost | Maximum Cost | Required. Safe integer; minimum 1; maximum 9007199254740991. |
| seed | Optional numeric seed; takes precedence over context randomness. Without either, use the fixed tool.io default seed. | Optional. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| universe | Universe | Required. Array of Safe integer; minimum 0; maximum 63.; minimum items 1; maximum items 64. |
| subsets | Subsets | Required. Array of Array of Safe integer; minimum 0; maximum 63.; minimum items 1; maximum items 64.; minimum items 1; maximum items 128. |
| costs | Costs | Required. Array of Safe integer; minimum 1; maximum 9007199254740991.; minimum items 1; maximum items 128. |
| witnessIndices | Witness Indices | Required. Array of Safe integer; minimum 0; maximum 127.; minimum items 1; maximum items 64. |
| witnessCost | Witness Cost | Required. Safe integer; minimum 1; maximum 9007199254740991. |
| randomness | Replay metadata: source is seed or context; seed is the normalized 32-bit seed or null for a context source. | Required. Object; no unknown keys. |
| randomness.seed | Optional numeric replay seed; normalization and precedence are explained below. | Required. Safe integer. or Null. |
| randomness.source | Source | Required. Text; one of "context", "seed". |
An explicit safe-integer seed takes precedence over injected context randomness and is normalized to an unsigned 32-bit integer. With no seed and no context source, replay uses the fixed tool.io default seed. A context source must return finite values from zero inclusive to one exclusive; its advancing state must be retained separately. randomness records the source and normalized seed, or null for context. These generators are not cryptographic random sources.
{
"input": {
"universeSize": 6,
"setCount": 5,
"plantedSetCount": 2,
"extraInclusionProbability": 0.4,
"minimumCost": 2,
"maximumCost": 9,
"seed": 42
},
"output": {
"universe": [
0,
1,
2,
3,
4,
5
],
"subsets": [
[
1,
5
],
[
0,
2,
3,
4
],
[
1,
4,
5
],
[
3
],
[
0,
2,
3,
4,
5
]
],
"witnessIndices": [
0,
1
],
"costs": [
8,
6,
2,
3,
8
],
"witnessCost": 14,
"randomness": {
"seed": 42,
"source": "seed"
}
}
}Limitations and assumptions
- The witness covers each element once, although the covering problem permits overlap. No minimum-cost cover is solved, and the planted construction is not a uniform sample of all feasible covering instances.
- A replay requires the same complete input and implementation. Randomized construction does not guarantee uniform coverage of every feasible output; finite samples can repeat unless a distinct-selection rule is explicitly stated.
- The field tables state structural bounds; cross-field constraints and bounded search or output budgets also apply. Unknown keys are rejected where the object contract disallows them. Input errors are distinct from null fields and deliberate invalid controls in a successful output.
Alternative or Complementary methods
For a supplied example, inspect the returned construction or delegated check directly. To evaluate a consumer, also test cases chosen for its own boundaries; a generated finite corpus does not establish exhaustive coverage.
References
Similar or alternative tools
- Random Set Partitioning Instance Generator
Generate a nonempty finite subset family and positive costs with a planted exact-once partition witness; every element must occur exactly once in a feasible selection, duplicate columns allowed, with no minimum-cost claim.
- Random Interval Scheduling Challenge Generator
Generate synthetic positive-duration half-open jobs and solve the declared count or weight objective exactly with finish-time dynamic programming, retaining one optimum with exclusion on objective ties.