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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 (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:

  • ax (Axes | None, default: None ) –

    Matplotlib axes to draw on. Creates a new figure if None.

Returns:

  • Axes –

    The axes with the plot.

to_string() -> str

Return a string describing the data.

Returns:

  • 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:

  • 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.

Returns:

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:

  • n_elements (int, default: 5 ) –

    Number of elements in the universe, by default 5.

  • n_subsets (int, default: 8 ) –

    Number of subsets, by default 8.

  • density (float, default: 0.3 ) –

    Probability that an element is included in a subset, by default 0.3.

  • seed (int | None, default: None ) –

    Random seed for reproducibility, by default None.

Returns:

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:

Returns:

  • str –

    String representation of the formulation.

formulate(data: SetPackingData) -> Model staticmethod

Formulate the Set Packing Problem using constraint-based approach.

Parameters:

Returns:

  • Model –

    A LunaModel ready to be solved.

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

Extract solution from quantum result.

Parameters:

  • solution (Solution) –

    The quantum solution.

  • data (SetPackingData) –

    The problem data.

Returns:

Solution

Solution model for SetPacking use case.

SetPackingSolution

Bases: UcSolution

Solution for the Set Packing Problem.

Attributes:

  • 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:

  • data (SetPackingData | None, default: None ) –

    Problem data for context.

  • ax (Axes | None, default: None ) –

    Matplotlib axes to draw on. Creates a new figure if None.

Returns:

  • Axes –

    The axes with the plot.

to_string() -> str

Return a string describing the solution.

Returns:

  • 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:

  • min_num_elements (int | None, default: None ) –

    Minimum number of elements per instance.

  • max_num_elements (int | None, default: None ) –

    Maximum number of elements per instance.

  • num_instances (int, default: 1 ) –

    Number of instances per size, by default 1.

  • density (float, default: 0.3 ) –

    Probability that an element is included in a subset, by default 0.3.

  • subset_ratio (float, default: 1.6 ) –

    Ratio of subsets to elements, by default 1.6.

  • seed (int | None, default: None ) –

    Random seed for reproducibility, by default None.

  • sizes (Sequence[int] | None, default: 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.

Returns:

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:

  • max_runtime (float, default: 3600 ) –

    SCIP time limit per instance in seconds. Must be positive. Defaults to 3600 seconds.

  • quiet (bool, default: True ) –

    Suppress the SCIP solver output.

Returns:

  • 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: