Multifit algorithm

An approximation algorithm for identical-machine makespan scheduling that repeatedly runs first-fit-decreasing bin packing while binary-searching a trial capacity.

Version

v1 · 2026-09-08 · History

Domain-specific #

5692

Origin domain

scheduling and partition algorithms

Subdomain

scheduling and partition algorithms

Core Idea

Multifit partitions job sizes among a fixed number of machines by treating a candidate makespan as bin capacity and using FFD feasibility as the search oracle. Lower and upper makespan bounds initialize a capacity interval; FFD packs jobs at each midpoint, success or failure updates the interval, and the best discovered partition supplies the schedule. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

Scope of Application

Multifit algorithm belongs to scheduling and partition algorithms and is useful where the analyst can specify the typed scheduling and partition algorithms carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate job sizes, machine count, initial bounds, FFD ordering and tie rules, iteration or tolerance limit, feasibility test, and approximation guarantee are explicit. The scope is broad within that domain but bounded by the need for job sizes, machine count, initial bounds, FFD ordering and tie rules, iteration or tolerance limit, feasibility test, and approximation guarantee are explicit. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.

Clarity

The abstraction clarifies a crowded vocabulary by making job sizes, machine count, initial bounds, FFD ordering and tie rules, iteration or tolerance limit, feasibility test, and approximation guarantee are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Multifit algorithm can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.

Manages Complexity

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Multifit algorithm. Multifit algorithm compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning

1. Identify the carrier. State what the elements, states, objects, or observations are: the typed scheduling and partition algorithms carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express job sizes, machine count, initial bounds, FFD ordering and tie rules, iteration or tolerance limit, feasibility test, and approximation guarantee are explicit independently of one notation or implementation.

Knowledge Transfer

Knowledge transfers strongly among subfields of scheduling and partition algorithms because they reuse the typed scheduling and partition algorithms carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, Lower and upper makespan bounds initialize a capacity interval; FFD packs jobs at each midpoint, success or failure updates the interval, and the best discovered partition supplies the schedule., and type the carrier, state every parameter and convention in the definition, test that job sizes, machine count, initial bounds, FFD ordering and tie rules, iteration or tolerance limit, feasibility test, and approximation guarantee are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions

Current abstraction Multifit algorithm Domain-specific

Parents (1) — more general patterns this builds on

• Multifit algorithm is a kind of Approximation Prime

  The proposed strict upward parent is prime:approximation.

Hierarchy path (1) — routes to 1 parentless root

• Multifit algorithm → Approximation → Representation → Abstraction

Neighborhood in Abstraction Space

Multifit algorithm sits in a moderately populated region (45^th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Combinatorial Optimization & Network Flows (24 abstractions)

Nearest neighbors

• Makespan — 0.91
• Single-machine scheduling — 0.90
• Prune and search — 0.89
• Parallel algorithm — 0.89
• Maximum satisfiability problem — 0.88

Computed from structural-signature embeddings · 2026-09-08