Strong NP-completeness¶

In computational complexity, strong NP-completeness is a property of computational problems that is a special case of NP-completeness.

Version: v1 · 2026-09-28 · History
Domain-specific #: 12324
Domain group: Applied Sciences & Engineering
Origin domain: Computer Science & Software Engineering
Subdomain: Computational Complexity → Computer Science & Software Engineering

Core Idea¶

Strong NP-completeness is treated here as the recurring computerscienceandinformation identity summarized by this source-grounded definition: In computational complexity, strong NP-completeness is a property of computational problems that is a special case of NP-completeness. In computational complexity, strong NP-completeness is a property of computational problems that is a special case of NP-completeness. A general computational problem may have numerical parameters. For example, the input to the bin packing problem is a list of objects of specific sizes and a size for the bins that must contain the objects—these object sizes and bin size are numerical.

Scope of Application¶

Documented setting. This pseudo-polynomial reduction is more restrictive than the usual poly-time reduction used for NP-hardness proofs.
Documented setting. From a theoretical perspective any strongly NP-hard optimization problem with a polynomially bounded objective function cannot have a fully polynomial-time approximation scheme (or FPTAS) unless P = NP.
Documented setting. Some strongly NP-complete problems may still be easy to solve on average, but it's more likely that difficult instances will be encountered in practice.
Documented setting. In computational complexity, strong NP-completeness is a property of computational problems that is a special case of NP-completeness.
Documented setting. For example, the input to the bin packing problem is a list of objects of specific sizes and a size for the bins that must contain the objects—these object sizes.

Clarity¶

A clear use of Strong NP-completeness names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In computational complexity, strong NP-completeness is a property of computational problems that is a special case of NP-completeness.

Manages Complexity¶

Strong NP-completeness compresses multiple computerscienceandinformation details into a stable diagnostic relation. The source shows both the central mechanism—in particular, the pseudo-polynomial reduction cannot output a numerical parameter that is not polynomially bounded by the size and value of numbers in the input.—and the practical consequence—for example, the input to the bin packing problem is a list of objects of specific sizes and a size for the bins.

Abstract Reasoning¶

Type the carrier. Identify the computerscienceandinformation entities to which the claim applies.
State the relation. Use the source-grounded identity: In computational complexity, strong NP-completeness is a property of computational problems that is a special case of NP-completeness.
Check operation and conditions. If we redefine the problem to have the parameters given in unary notation, then the parameters must be bounded by the input size.
Demand recognition evidence.

Knowledge Transfer¶

Within the home domain. Knowledge about Strong NP-completeness transfers literally when a new case preserves the same carrier type, relation, and recognition test. This pseudo-polynomial reduction is more restrictive than the usual poly-time reduction used for NP-hardness proofs. From a theoretical perspective any strongly NP-hard optimization problem with a polynomially bounded objective function cannot have a fully polynomial-time approximation scheme (or FPTAS) unless P = NP. Beyond the home domain. No canonical parent is asserted for Strong NP-completeness.

Relationships to Other Abstractions¶

Current abstraction Strong NP-completeness Domain-specific

Parents (1) — more general patterns this builds on

Strong NP-completeness presupposes Complexity Class Domain-specific

Strong NP-completeness is defined through NP-completeness under restrictions on numerical encoding and therefore presupposes the class structure.

Neighborhood in Abstraction Space¶

Strong NP-completeness sits in a moderately populated region (58^th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Unclustered & Miscellaneous (2551 abstractions)

Nearest neighbors

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