Set Packing API Reference

Data

Data model for SetPacking use case.

`SetPackingData`

Bases: UcData

Data for the Set Packing Problem.

Given a universe of elements, a collection of subsets, and weights per subset, the Set Packing problem asks to find the maximum-weight collection of pairwise disjoint subsets.

Attributes:

Name	Type	Description
`name`	`Literal['set_packing']`	Identifier for this data type.
`subset_matrix`	`list[list[int]]`	A matrix where each row represents a subset and each column an element. `subset_matrix[i][j] = 1` if subset i contains element j, 0 otherwise.
`weights`	`list[float]`	Weight (value) associated with each subset.

`plot(*, ax: Axes | None = None) -> Axes`

Plot the subset matrix as a binary heatmap with weights.

Parameters:

Name	Type	Description	Default
`ax`	`Axes \| None`	Matplotlib axes to draw on. Creates a new figure if `None`.	`None`

Returns:

Type	Description
`Axes`	The axes with the plot.

`to_string() -> str`

Return a string describing the data.

Returns:

Type	Description
`str`	String representation of the data.

`from_values(subset_matrix: list[list[int]], weights: list[float]) -> SetPackingData` `staticmethod`

Create a SetPackingData instance from explicit values.

Parameters:

Name	Type	Description	Default
`subset_matrix`	`list[list[int]]`	A matrix where each row represents a subset and each column an element. `subset_matrix[i][j] = 1` if subset i contains element j, 0 otherwise.	required
`weights`	`list[float]`	Weight (value) associated with each subset.	required

Returns:

Type	Description
`SetPackingData`	A SetPackingData instance with the given values.

`generate_random(n_elements: int = 5, n_subsets: int = 8, density: float = 0.3, seed: int | None = None) -> SetPackingData` `staticmethod`

Generate a random set packing instance.

Parameters:

Name	Type	Description	Default
`n_elements`	`int`	Number of elements in the universe, by default 5.	`5`
`n_subsets`	`int`	Number of subsets, by default 8.	`8`
`density`	`float`	Probability that an element is included in a subset, by default 0.3.	`0.3`
`seed`	`int \| None`	Random seed for reproducibility, by default None.	`None`

Returns:

Type	Description
`SetPackingData`	A randomly generated set packing instance.

Formulation

Formulation for SetPacking use case.

`SetPackingFormulation`

Bases: UcFormulation[SetPackingData, SetPackingSolution]

Constraint-based formulation for the Set Packing Problem.

Mathematical Formulation

Decision Variables:
    x_s in {0,1} for each subset s: 1 if subset s is selected

Objective:
    maximize sum_s weights[s] * x_s

Constraints:
    For each element e:
        sum_{s containing e} x_s <= 1
    (each element can be in at most one selected subset)

`to_string(data: SetPackingData) -> str` `staticmethod`

Return a string describing the formulation.

Parameters:

Name	Type	Description	Default
`data`	`SetPackingData`	The problem data.	required

Returns:

Type	Description
`str`	String representation of the formulation.

`formulate(data: SetPackingData) -> Model` `staticmethod`

Formulate the Set Packing Problem using constraint-based approach.

Parameters:

Name	Type	Description	Default
`data`	`SetPackingData`	The Set Packing instance data.	required

Returns:

Type	Description
`Model`	A LunaModel ready to be solved.

`interpret(solution: Solution, data: SetPackingData) -> SetPackingSolution` `staticmethod`

Extract solution from quantum result.

Parameters:

Name	Type	Description	Default
`solution`	`Solution`	The quantum solution.	required
`data`	`SetPackingData`	The problem data.	required

Returns:

Type	Description
`SetPackingSolution`	Structured solution with metrics.

Solution

Solution model for SetPacking use case.

`SetPackingSolution`

Bases: UcSolution

Solution for the Set Packing Problem.

Attributes:

Name	Type	Description
`name`	`Literal['set_packing']`	Identifier for this solution type.
`selected_subsets`	`list[int]`	Indices of selected subsets.
`total_weight`	`float`	Total weight of selected subsets.
`is_valid`	`bool`	Whether selected subsets are pairwise disjoint.

`plot(data: SetPackingData | None = None, *, ax: Axes | None = None) -> Axes`

Plot the set packing solution.

Parameters:

Name	Type	Description	Default
`data`	`SetPackingData \| None`	Problem data for context.	`None`
`ax`	`Axes \| None`	Matplotlib axes to draw on. Creates a new figure if `None`.	`None`

Returns:

Type	Description
`Axes`	The axes with the plot.

`to_string() -> str`

Return a string describing the solution.

Returns:

Type	Description
`str`	String representation of the solution.

Instance

Instance model for SetPacking use case.

`SetPackingInstance`

Bases: UcInstance[SetPackingData, SetPackingFormulation, SetPackingSolution]

Instance combining data and formulation for SetPacking.

Collection

Collection of SetPacking instances.

`SetPackingCollection`

Bases: UcInstanceCollection[SetPackingInstance]

Collection of Set Packing instances.

This collection provides methods to generate benchmark instances with various characteristics for testing and evaluation.

`from_random(min_num_elements: int | None = None, max_num_elements: int | None = None, num_instances: int = 1, *, sizes: Sequence[int] | None = None, density: float = 0.3, subset_ratio: float = 1.6, seed: int | None = None) -> SetPackingCollection` `classmethod`

Generate random set packing instances.

Parameters:

Name	Type	Description	Default
`min_num_elements`	`int \| None`	Minimum number of elements per instance.	`None`
`max_num_elements`	`int \| None`	Maximum number of elements per instance.	`None`
`num_instances`	`int`	Number of instances per size, by default 1.	`1`
`density`	`float`	Probability that an element is included in a subset, by default 0.3.	`0.3`
`subset_ratio`	`float`	Ratio of subsets to elements, by default 1.6.	`1.6`
`seed`	`int \| None`	Random seed for reproducibility, by default None.	`None`
`sizes`	`Sequence[int] \| None`	Explicit sizes to generate, e.g. `[10, 50, 100]`, instead of a range. Mutually exclusive with `min_num_elements`/`max_num_elements`, by default None.	`None`

Returns:

Type	Description
`SetPackingCollection`	Collection containing generated instances.

`filter_infeasible(max_runtime: float = 3600, *, quiet: bool = True) -> list[bool]`

Drop the instances of this collection that have no feasible solution.

Every instance is formulated and handed to SCIP, which stops as soon as it finds the first feasible solution. An instance is removed from the collection when SCIP proves the model infeasible, when no solution turns up within max_runtime, or when formulating it fails altogether. This keeps randomly generated instances from breaking a downstream pipeline.

Parameters:

Name	Type	Description	Default
`max_runtime`	`float`	SCIP time limit per instance in seconds. Must be positive. Defaults to 3600 seconds.	`3600`
`quiet`	`bool`	Suppress the SCIP solver output.	`True`

Returns:

Type	Description
`list[bool]`	Feasibility mask over the instances as they were before filtering, in that order: `True` where the instance was kept, `False` where it was removed.

Raises:

Type	Description
`ValueError`	If `max_runtime` is not positive.

Set Packing API Reference

Data

SetPackingData

plot(*, ax: Axes | None = None) -> Axes

to_string() -> str

from_values(subset_matrix: list[list[int]], weights: list[float]) -> SetPackingData staticmethod

generate_random(n_elements: int = 5, n_subsets: int = 8, density: float = 0.3, seed: int | None = None) -> SetPackingData staticmethod

Formulation

SetPackingFormulation

to_string(data: SetPackingData) -> str staticmethod

formulate(data: SetPackingData) -> Model staticmethod

interpret(solution: Solution, data: SetPackingData) -> SetPackingSolution staticmethod

Solution

SetPackingSolution

plot(data: SetPackingData | None = None, *, ax: Axes | None = None) -> Axes

to_string() -> str

Instance

SetPackingInstance

Collection

SetPackingCollection

from_random(min_num_elements: int | None = None, max_num_elements: int | None = None, num_instances: int = 1, *, sizes: Sequence[int] | None = None, density: float = 0.3, subset_ratio: float = 1.6, seed: int | None = None) -> SetPackingCollection classmethod

filter_infeasible(max_runtime: float = 3600, *, quiet: bool = True) -> list[bool]

`SetPackingData`

`plot(*, ax: Axes | None = None) -> Axes`

`to_string() -> str`

`from_values(subset_matrix: list[list[int]], weights: list[float]) -> SetPackingData` `staticmethod`

`generate_random(n_elements: int = 5, n_subsets: int = 8, density: float = 0.3, seed: int | None = None) -> SetPackingData` `staticmethod`

`SetPackingFormulation`

`to_string(data: SetPackingData) -> str` `staticmethod`

`formulate(data: SetPackingData) -> Model` `staticmethod`

`interpret(solution: Solution, data: SetPackingData) -> SetPackingSolution` `staticmethod`

`SetPackingSolution`

`plot(data: SetPackingData | None = None, *, ax: Axes | None = None) -> Axes`

`to_string() -> str`

`SetPackingInstance`

`SetPackingCollection`

`from_random(min_num_elements: int | None = None, max_num_elements: int | None = None, num_instances: int = 1, *, sizes: Sequence[int] | None = None, density: float = 0.3, subset_ratio: float = 1.6, seed: int | None = None) -> SetPackingCollection` `classmethod`

`filter_infeasible(max_runtime: float = 3600, *, quiet: bool = True) -> list[bool]`