science

Steiner travelling salesman problem

Steiner travelling salesman problem is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Steiner travelling salesman problem rather than just read about it. In short: The Steiner traveling salesman problem (Steiner TSP, or STSP) is an extension of the traveling salesman problem. Given a list of cities, some of which are required, and the lengths of the roads between them, the goal is to find the shortest possible walk that visits each required city and then returns to the origin city.

Key takeaways

Steiner travelling salesman problem belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Steiner travelling salesman problem to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Steiner travelling salesman problem from memory before moving on to harder problems.

Reference excerpt

The Steiner traveling salesman problem (Steiner TSP, or STSP) is an extension of the traveling salesman problem. Given a list of cities, some of which are required, and the lengths of the roads between them, the goal is to find the shortest possible walk that visits each required city and then returns to the origin city. During a walk, vertices can be visited more than once, and edges may be traversed more than once.

References

M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, 1979. Huili Zhang, Weitian Tong, Yinfeng Xu, and Guohui Lin. The steiner traveling salesman problem with online edge blockages. European Journal of Operational Research, 243(1):30–40, 2015. Gerard Cornuejols, Jean Fonlupt, and Denis Naddef. The traveling salesman problem on a graph and some related integer polyhedra. Mathematical Programming, 33(1):1–27, 1985. S. Borne, A.R. Mahjoub, and R. Taktak. A branch-and-cut algorithm for the multiple steiner TSP with order constraints. Electronic Notes in Discrete Mathematics, 41:487–494, 2013. Huili Zhang, Weitian Tong, Yinfeng Xu, and Guohui Lin. The steiner traveling salesman problem with online advanced edge blockages. Computers & Operations Research, 70:26–38, 2016. Adam N. Letchford, Saeideh D. Nasiri, and Dirk Oliver Theis. Compact formulations of the steiner traveling salesman problem and related problems. European Journal of Operational Research, 228(1):83–92, 2013. Adam N. Letchford and Saeideh D. Nasiri. The steiner travelling salesman problem with correlated costs. European Journal of Operational Research, 245(1):62–69, 2015. Juan-Jos´e Salazar-Gonz´alez. The steiner cycle polytope. European Journal of Operational Research, 147(3):671–679, 2003.

Worked examples

Example 1 — a first encounter with Steiner travelling salesman problem

Start with the simplest possible case. Write down what Steiner travelling salesman problem claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Steiner travelling salesman problem before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Steiner travelling salesman problem ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Steiner travelling salesman problem

In research: Steiner travelling salesman problem appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Steiner travelling salesman problem in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Steiner travelling salesman problem is common in secondary-school and first-year university syllabi. It links to neighbouring topics Combinatorial optimization, Graph theory stubs, so understanding it makes those chapters shorter.
In everyday life: Look for Steiner travelling salesman problem outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Steiner travelling salesman problem in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Steiner travelling salesman problem means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Steiner travelling salesman problem out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Steiner travelling salesman problem in simple terms?

Why does Steiner travelling salesman problem matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Steiner travelling salesman problem?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Steiner travelling salesman problem.