Skip to content

In-Place Algorithm

An algorithm that replaces its designated input with the result while using only a constant number of auxiliary units under a stated memory model.

Version
v1 · 2026-10-17 · History
Domain-specific #
14188
Domain group
Applied Sciences & Engineering
Origin domain
Computer Science & Software Engineering
Subdomain
Space Efficient Algorithms → Computer Science & Software Engineering

Core Idea

An in-place algorithm, in this strict sense, replaces its designated input with the result while using a constant number of counted auxiliary units under a stated memory model. Its transformation, buffer, result, units, and overwrite schedule must be identifiable. Constantly many array indices use O(log n) bits; O(1) ring elements is a different claim, not an equivalent bit bound.[ref-7bc7d83ed44d][ref-0fe4154ac5b2]

Scope of Application

Two cited cases use unlike operations and accounting units:

  • Array permutation. Dudek, Gawrychowski and Pokorski rearrange an array in its own storage using cycles and constantly many input-size indices. Their O(log n)-bit bound depends on permutation-access assumptions.[^ref-7bc7d83ed44d]
  • Algebraic transform. Harvey and Roche's forward truncated Fourier transform overwrites one coefficient buffer using O(1) auxiliary ring elements and pointers under ring and root assumptions. It gives no model-independent bit bound.[^ref-0fe4154ac5b2]

These establish a narrow subtype, not a property of every sorting or transform procedure.

Clarity

Ask where the result is written and what storage computation uses. A new output array fails the same-buffer condition. FFTW 2 documents an FFTW_IN_PLACE path that computes in a temporary array before copying back: final address alone proves no constant auxiliary bound.[^ref-6a135b73a262] Harvey and Roche's separate-output polynomial multiplication uses O(1) auxiliary units but is out of place.[^ref-0fe4154ac5b2]

Manages Complexity

The roles separate output placement, auxiliary accounting, and dependencies. In a permutation, values move through cycles without a growing second array; recognizing cycles within the index budget affects running time. Dudek and colleagues achieve a subquadratic strict-space method under their assumptions, disproving a universal quadratic-time penalty.[^ref-7bc7d83ed44d] A truncated Fourier transform needs a different overwrite schedule; neither case supplies a universal recipe.[^ref-0fe4154ac5b2]

Abstract Reasoning

For a proposed algorithm, name the input and result; inventory scratch arrays, indices, pointers, elements, and stacks; then state the unit and prove its counted quantity stays constant as input grows. Check that overwrites preserve needed values. Looser “in place” usage allows growing extra space, so report the actual bound. No general speed or parallelism advantage follows.[ref-7bc7d83ed44d][ref-0fe4154ac5b2]

Knowledge Transfer

The diagnostic transfers across permutation and transform despite different operations and units. Both are Algorithms with output-location and storage constraints. In Situ concerns an original setting, not a buffer. In-Place Adjacent Block Rotation specifies a narrower AB-to-BA task. The transferable question is buffer and budget, not the particular technique.

Relationships to Other Abstractions

Local relationship map for In-Place AlgorithmParents appear above the current abstraction, mutual partners to the right, and children below. Node labels state whether each abstraction is prime or domain-specific; colors identify relation types.In-Place AlgorithmDOMAINPrime abstraction: Algorithm — is a kind ofAlgorithmPRIME

Current abstraction In-Place Algorithm Domain-specific

Parents (1) — more general patterns this builds on

  • In-Place Algorithm is a kind of Algorithm Prime

    A strict in-place algorithm is an algorithm distinguished by same-buffer output and a constant counted auxiliary-unit budget.

Hierarchy path (1) — routes to 1 parentless root

Neighborhood in Abstraction Space

In-Place Algorithm sits in a sparse region of the domain-specific corpus (63rd percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Program Execution & Runtime Concepts (34 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-17

References

[^ref-7bc7d83ed44d]: Bartłomiej Dudek, Paweł Gawrychowski and Karol Pokorski, Strictly In-Place Algorithms for Permuting and Inverting Permutations, 2021, abstract and Introduction, PDF pp. 1–3. Original algorithm paper; strict O(log n)-bit/constant-index definition, cycle methods, access assumptions and problem-bounded time comparison. [^ref-0fe4154ac5b2]: David Harvey and Daniel S. Roche, An in-place truncated Fourier transform and applications to polynomial multiplication, 2010, §§1.3, 2.1, 3 and 6, PDF pp. 2–5. Original algorithm paper; one-buffer versus separate-output definitions, ring-element/pointer model, transform and multiplication boundary. [^ref-6a135b73a262]: FFTW project, FFTW 2 Reference Manual, “Plan Creation,” FFTW_IN_PLACE option. Original software manual; documented temporary-array fallback for the FFTW 2 API. No inference about other versions.