Steiner tree problem

E530318

NP-hard problem combinatorial optimization problem geometric optimization problem graph theory problem

The Steiner tree problem is a classic optimization problem in combinatorial mathematics and computer science that seeks the shortest network of line segments connecting a given set of points, potentially adding extra intermediate points to minimize total length.

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All labels observed (6)

Label	Occurrences
Steiner tree problem canonical	2
Steiner Tree problem (decision version)	1
Steiner minimal tree problem	1
Steiner tree	1
Steiner tree in series-parallel graphs	1
Steiner tree problem in graphs	1

How this entity was disambiguated

This entity first appeared as the object of triple T5570708 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Steiner tree problem
Context triple: [Fermat point, relatedConcept, Steiner tree problem]

A. Kruskal
Kruskal is a surname most prominently associated with American mathematician Martin David Kruskal, known for his work in soliton theory and nonlinear science.
B. Dijkstra
Dijkstra is a renowned Dutch computer scientist best known for his pioneering work in algorithms, including Dijkstra's shortest path algorithm, and for his influential contributions to programming methodology and software engineering.
C. Fermat point
The Fermat point is a special point inside a triangle that minimizes the total distance to the triangle’s three vertices.
D. Eppstein
Eppstein is a small historic town in the German state of Hesse, known for its medieval castle and scenic location in the Taunus mountains.
E. Conway's 99-graph problem
Conway's 99-graph problem is an unsolved combinatorial question in graph theory, posed by John H. Conway, concerning the existence and properties of a hypothetical 99-vertex graph with highly constrained adjacency conditions.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Steiner tree problem
Target entity description: The Steiner tree problem is a classic optimization problem in combinatorial mathematics and computer science that seeks the shortest network of line segments connecting a given set of points, potentially adding extra intermediate points to minimize total length.

A. Kruskal
Kruskal is a surname most prominently associated with American mathematician Martin David Kruskal, known for his work in soliton theory and nonlinear science.
B. Dijkstra
Dijkstra is a renowned Dutch computer scientist best known for his pioneering work in algorithms, including Dijkstra's shortest path algorithm, and for his influential contributions to programming methodology and software engineering.
C. Fermat point
The Fermat point is a special point inside a triangle that minimizes the total distance to the triangle’s three vertices.
D. Eppstein
Eppstein is a small historic town in the German state of Hesse, known for its medieval castle and scenic location in the Taunus mountains.
E. Conway's 99-graph problem
Conway's 99-graph problem is an unsolved combinatorial question in graph theory, posed by John H. Conway, concerning the existence and properties of a hypothetical 99-vertex graph with highly constrained adjacency conditions.
F. None of above. chosen

Statements (49)

Predicate	Object
instanceOf	NP-hard problem ⓘ combinatorial optimization problem ⓘ geometric optimization problem ⓘ graph theory problem ⓘ
allows	introduction of additional intermediate points ⓘ
alsoCalled	Steiner minimal tree problem ⓘ linked to: Steiner tree problem
complexityClass	NP-complete in graphs ⓘ NP-hard in Euclidean plane ⓘ
constraint	all terminal points must be connected ⓘ resulting network must be a tree ⓘ
edgeWeights	can represent Euclidean distances ⓘ can represent arbitrary nonnegative costs ⓘ
field	combinatorics ⓘ operations research ⓘ theoretical computer science ⓘ
goal	find a minimum-length network connecting a given set of points ⓘ
hasApproximation	polynomial-time approximation schemes in some metric spaces ⓘ
hasProperty	admits approximation algorithms ⓘ admits heuristic algorithms ⓘ exact solution is computationally expensive for large instances ⓘ generalizes the minimum spanning tree problem ⓘ
hasSpecialCase	Steiner tree in series-parallel graphs ⓘ linked to: Steiner tree problem Steiner tree in trees (polynomial-time solvable) ⓘ
hasVariant	Euclidean Steiner tree problem ⓘ Steiner forest problem ⓘ Steiner tree problem in graphs ⓘ linked to: Steiner tree problem directed Steiner tree problem ⓘ group Steiner tree problem ⓘ rectilinear Steiner tree problem ⓘ
historicalOrigin	19th century geometry ⓘ
input	finite set of terminal vertices ⓘ underlying metric space or graph ⓘ
namedAfter	Jakob Steiner ⓘ
objectiveFunction	total length of edges in the connecting network ⓘ
optimizationType	minimization problem ⓘ
output	set of Steiner points that minimize total length ⓘ tree of minimum total edge length connecting all terminals ⓘ
relatedTo	Steiner system ⓘ minimum spanning tree problem ⓘ shortest path problem ⓘ
solutionStructure	Steiner points in Euclidean plane have degree 3 ⓘ angles at Steiner points in Euclidean plane are 120 degrees apart ⓘ
studiedIn	algorithm design ⓘ computational geometry ⓘ
usedIn	VLSI design ⓘ network design ⓘ phylogenetic tree reconstruction ⓘ transportation network planning ⓘ wireless communication networks ⓘ

How these facts were elicited

Referenced by (7)

Full triples — surface form annotated when it differs from this entity's canonical label.

Fermat point → relatedConcept → Steiner tree problem ⓘ

Reducibility Among Combinatorial Problems → establishesNPCompletenessOf → Steiner Tree problem (decision version) ⓘ

subject linked to: "Reducibility Among Combinatorial Problems" (1972)