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Uniform-machines scheduling

In the specific variant called uniform machine scheduling, some machines are uniformly faster than others.

Version
v1 · 2026-09-28 · History
Domain-specific #
12702
Domain group
Formal Sciences
Origin domain
Operations Research
Subdomain
Scheduling Theory → Operations Research

Core Idea

Uniform-machines scheduling is treated here as the recurring scheduling theory identity summarized by this source-grounded definition: In the specific variant called uniform machine scheduling, some machines are uniformly faster than others. Uniform machine scheduling (also called uniformly-related machine scheduling or related machine scheduling) is an optimization problem in computer science and operations research. It is a variant of optimal job scheduling. We are given n jobs J 1 , J 2 , ..., J n of varying processing times, which need to be scheduled on m different machines.

Scope of Application

  • Minimizing the weighted-average completion time. Epstein and Sgall generalized the PTAS for uniform machines to handle more general objective functions.

  • Minimizing the weighted-average completion time. Instead of minimizing the objective function max(C i ), one can minimize the objective function max(f(C i )), where f is any fixed function.

  • Minimizing the weighted-average completion time. Similarly, one can minimize the objective function sum(f(C i )).

  • AlgorithmsMinimizing the average completion time. The SPT algorithm (Shortest Processing Time First), sorts the jobs by their length, shortest first, and then assigns them to the processor with the earliest end time so far.

  • AlgorithmsMinimizing the average completion time. It runs in time O(n log n), and minimizes the average completion time on identical machines, P|| \sum Ci .

Clarity

A clear use of Uniform-machines scheduling names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In the specific variant called uniform machine scheduling, some machines are uniformly faster than others. The strongest recognition evidence in the frozen account is: Minimizing the weighted average completion time is NP-hard even on identical machines, by reduction from the knapsack problem.

Manages Complexity

Uniform-machines scheduling compresses multiple scheduling theory details into a stable diagnostic relation. The source shows both the central mechanism—a constant-factor approximation is attained by the Longest-processing-time-first algorithm (LPT).—and the practical consequence—minimizing the maximum completion time is NP-hard even for identical machines, by reduction from the partition problem. This compression makes cases comparable while leaving parameters, conventions, exceptions, and evidential quality explicit.

Abstract Reasoning

  1. Type the carrier. Identify the scheduling theory entities to which the claim applies.
  2. State the relation. Use the source-grounded identity: In the specific variant called uniform machine scheduling, some machines are uniformly faster than others.
  3. Check operation and conditions. The time that machine i needs in order to process job j is denoted by p i,j .
  4. Demand recognition evidence. Minimizing the weighted average completion time is NP-hard even on identical machines, by reduction from the knapsack problem.
  5. Test variation.

Knowledge Transfer

Within the home domain. Knowledge about Uniform-machines scheduling transfers literally when a new case preserves the same carrier type, relation, and recognition test. Epstein and Sgall generalized the PTAS for uniform machines to handle more general objective functions. Instead of minimizing the objective function max(C i ), one can minimize the objective function max(f(C i )), where f is any fixed function. Beyond the home domain. No canonical parent is asserted for Uniform-machines scheduling.

Relationships to Other Abstractions

Local relationship map for Uniform-machines schedulingParents 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.Uniform-machinesschedulingDOMAINPrime abstraction: Scheduling — is a decomposition ofSchedulingPRIME

Current abstraction Uniform-machines scheduling Domain-specific

Parents (1) — more general patterns this builds on

  • Uniform-machines scheduling is a decomposition of Scheduling Prime

    Uniform-machine scheduling retains assignment and timing under resource constraints while specializing machines by speed.

Hierarchy paths (5) — routes to 3 parentless roots

Neighborhood in Abstraction Space

Uniform-machines scheduling sits in a sparse region of the domain-specific corpus (68th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Unclustered & Miscellaneous (2551 abstractions)

Nearest neighbors

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