Strip packing problem¶

The strip packing problem is a 2-dimensional geometric minimization problem.

Version: v1 · 2026-09-28 · History
Domain-specific #: 12320
Domain group: Formal Sciences
Origin domain: Operations Research
Subdomains: Packing Problems, Combinatorial Optimization → Operations Research

Core Idea¶

Strip packing problem is treated here as the recurring mathematicslogicstatistics identity summarized by this source-grounded definition: The strip packing problem is a 2-dimensional geometric minimization problem. The strip packing problem is a 2-dimensional geometric minimization problem. Given a set of axis-aligned rectangles and a strip of bounded width and infinite height, determine an overlapping-free packing of the rectangles into the strip, minimizing its height. This problem is a cutting and packing problem and is classified as an Open Dimension Problem according to Wäscher et al.

Scope of Application¶

Variants. However, there are applications that have explicit requirements on the structure of the packing.
Definition. This definition is used for all polynomial time algorithms.
Definition. An instance I = (\mathcal{I},W) of the strip packing problem consists of a strip with width W = 1 and infinite height, as well as a set \mathcal{I} of rectangular.
Definition. Each item i \in \mathcal{I} has a width wi \in (0,1] \cap \mathbb{Q} and a height hi \in (0,1] \cap \mathbb{Q} .
Definition. A packing of the items is a mapping that maps each lower-left corner of an item i \in \mathcal{I} to a position (xi,yi) \in ([0,1-wi] \cap \mathbb{Q}).

Clarity¶

A clear use of Strip packing problem names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is The strip packing problem is a 2-dimensional geometric minimization problem. The strongest recognition evidence in the frozen account is: Geometry: In the standard variant of this problem, the set of given items consists of rectangles.

Manages Complexity¶

Strip packing problem compresses multiple mathematicslogicstatistics details into a stable diagnostic relation. The source shows both the central mechanism—an instance I = (\mathcal{I},W) of the strip packing problem consists of a strip with width W = 1 and infinite height, as well as a set \mathcal{I} of rectangular items.—and the practical consequence—one of these requirements is to be able to cut the items from the strip.

Abstract Reasoning¶

Type the carrier. Identify the mathematicslogicstatistics entities to which the claim applies.
State the relation. Use the source-grounded identity: The strip packing problem is a 2-dimensional geometric minimization problem.
Check operation and conditions. Especially the width of the strip is given by an arbitrary integer number larger than 1.
Demand recognition evidence. Geometry: In the standard variant of this problem, the set of given items consists of rectangles.
Test variation.

Knowledge Transfer¶

Within the home domain. Knowledge about Strip packing problem transfers literally when a new case preserves the same carrier type, relation, and recognition test. However, there are applications that have explicit requirements on the structure of the packing. This definition is used for all polynomial time algorithms. Beyond the home domain. No canonical parent is asserted for Strip packing problem. An outside case receives the specialist name only when the same typed roles and rejection conditions can be filled literally; otherwise the comparison remains an analogy pending later graph densification.

Relationships to Other Abstractions¶

Current abstraction Strip packing problem Domain-specific

Parents (1) — more general patterns this builds on

Strip packing problem is a kind of Packing Problem Domain-specific

It minimizes used strip height under geometric nonoverlap constraints.

Hierarchy path (1) — routes to 1 parentless root

Strip packing problem → Packing Problem → Optimization

Neighborhood in Abstraction Space¶

Strip packing problem sits in a crowded region of the domain-specific corpus (38^th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Combinatorial Optimization & Discrete Structures (31 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08