Set TSP problem

A traveling-salesman generalization seeking a minimum-cost tour that visits at least one vertex from every specified group.

Version

v1 · 2026-09-08 · History

Domain-specific #

6685

Origin domain

combinatorial optimization

Subdomain

combinatorial optimization

Aliases

Generalized TSP, Group TSP, One-of-a-set TSP, Covering salesman problem

Core Idea

Groups may be assumed disjoint after a stated reduction, the tour need not visit every vertex, directed metric and prize variants change the model and NP-hardness follows because singleton groups recover ordinary TSP. Candidate vertices are partitioned or covered by required sets; optimization jointly chooses a representative from each set and orders the chosen vertices into a closed tour minimizing edge cost. 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

Set TSP problem belongs to combinatorial optimization and is useful where the analyst can specify the typed combinatorial optimization carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, then evaluate the weighted graph or distance matrix and directedness, required vertex groups and disjointness convention, decision variables selecting vertices and edges, at-least-one-per-group coverage constraint, closed connected tour and subtour elimination, total-cost objective, ordinary TSP singleton special case, reductions and approximation assumptions and solution witness are explicit.

Clarity

The abstraction clarifies a crowded vocabulary by making the weighted graph or distance matrix and directedness, required vertex groups and disjointness convention, decision variables selecting vertices and edges, at-least-one-per-group coverage constraint, closed connected tour and subtour elimination, total-cost objective, ordinary TSP singleton special case, reductions and approximation assumptions and solution witness 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.

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 Set TSP problem. Set TSP problem 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 combinatorial optimization carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the weighted graph or distance matrix and directedness, required vertex groups and disjointness convention, decision variables selecting vertices and edges, at-least-one-per-group coverage constraint, closed connected tour and subtour elimination, total-cost objective, ordinary TSP singleton special case, reductions and approximation assumptions and solution witness are explicit independently of one notation or implementation.

Knowledge Transfer

Knowledge transfers strongly among subfields of combinatorial optimization because they reuse the typed combinatorial optimization carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, Candidate vertices are partitioned or covered by required sets; optimization jointly chooses a representative from each set and orders the chosen vertices into a closed tour minimizing edge cost., and type the carrier, state every parameter and convention in the definition, test that the weighted graph or distance matrix and directedness, required vertex groups and disjointness convention, decision variables selecting vertices and edges, at-least-one-per-group coverage constraint, closed connected tour and subtour elimination, total-cost objective, ordinary TSP singleton special case, reductions and approximation assumptions and solution witness are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions

Current abstraction Set TSP problem Domain-specific

Parents (1) — more general patterns this builds on

• Set TSP problem is a kind of Planning Prime

  The proposed strict upward parent is prime:planning.

Hierarchy path (1) — routes to 1 parentless root

• Set TSP problem → Planning → Foresight

Neighborhood in Abstraction Space

Set TSP problem sits in a crowded region of the domain-specific corpus (8^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 & Network Flows (24 abstractions)

Nearest neighbors

• 3-dimensional matching — 0.94
• Shortest path problem — 0.94
• Closure problem — 0.94
• Quasi-bipartite graph — 0.93
• Dissociation number — 0.93

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