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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 Luna Model 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, max_num_elements: int, num_instances: int = 1, *, 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) –

    Minimum number of elements per instance.

  • max_num_elements (int) –

    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.

Returns: