Set of test problems for the minimum length connection networks

Soukup, Jiří; Chow, William

doi:10.1145/1216969.1216975

Cited by 14 publications

(8 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The above relation fcr sl, as obtained for 3 nodes -see Equation (3), and the above relation for (s1+sz), as obtained for 4 nodes -see Equation (5), are only a special case of this rule.…”

Section: Figure 6 Model With a Rubber Membrane I F(z) Imentioning

confidence: 76%

Minimum Steiner trees, roots of a polynomial, and other magic

Soukup¹

1977

SIGMAP Bull.

Self Cite

View full text Add to dashboard Cite

Minimum Steiner trees~ roots of a polynomia!~ and other magic by J. Soukup, Bell-Northern Research, Ottawa Resume:The paper is a collection of observations and ideas on a surprising similarity between Steiner points on one hand, and roots of a complex polynomial on the other.These ideas can also be used to derive a simple practical method to generate good suboptimal Steiner trees. However, the main purpose of the paper is to point out a vast area of problems still open to further research. [s of a polynomial, derivative of a polynomial, systems of polynomial equations.i. -Relation between roots of f(z) and between the Steiner points.-Relations between the roots of f(z) and the roots of f (k~z) for a general k>l.The paper assumes the basic knowledge of the properties of the regular (euclidian distance) minimum Steiner trees.

show abstract

“…The above relation fcr sl, as obtained for 3 nodes -see Equation (3), and the above relation for (s1+sz), as obtained for 4 nodes -see Equation (5), are only a special case of this rule.…”

Section: Figure 6 Model With a Rubber Membrane I F(z) Imentioning

confidence: 76%

Minimum Steiner trees, roots of a polynomial, and other magic

Soukup¹

1977

SIGMAP Bull.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The first problems we consider are a subset of the 46 instances from Soukup and Chow [20], available from the OR-Library [4]. These are all planar instances (d = 2) with between 3 and 20 terminals, except for one problem with N = 62.…”

Section: Numerical Resultsmentioning

confidence: 99%

An improved algorithm for computing Steiner minimal trees in Euclidean d-space

Fampa

Anstreicher

2008

Discrete Optimization

View full text Add to dashboard Cite

We describe improvements to Smith's branch-and-bound (B&B) algorithm for the Euclidean Steiner problem in R d . Nodes in the B&B tree correspond to full Steiner topologies associated with a subset of the terminal nodes, and branching is accomplished by "merging" a new terminal node with each edge in the current Steiner tree. For a given topology we use a conic formulation for the problem of locating the Steiner points to obtain a rigorous lower bound on the minimal tree length. We also show how to obtain lower bounds on the child problems at a given node without actually computing the minimal Steiner trees associated with the child topologies. These lower bounds reduce the number of children created and also permit the implementation of a "strong branching" strategy that varies the order in which the terminal nodes are added. Computational results demonstrate substantial gains compared to Smith's original algorithm.

show abstract

“…fit was typically chosen to have an initial value of 0.2 and was decreased by a factor of 0.999 after every 20 iterations. Figure 8 shows the solutions obtained on a set of test examples from the literature (Soukup and Chow 1978). To the best of our knowledge, this is the only test set available in the literature for which the co-ordinates of the site points as well as the length of the minimal tree are available.…”

Section: Resultsmentioning

confidence: 99%

“…We are grateful to Prof. S. C. Dutta Roy for his valuable advice and critical appraisal of the manuscript, to Prof. J. Beasley of Imperial College for providing us with the benchmark set of 46 problems (Soukup and Chow 1978) and to Prof. D.J. Willshaw of Edinburgh College for providing the co-ordinates of the 100-point problem (Durbin and Willshaw 1987).…”

mentioning

confidence: 99%

A neural network for the Steiner minimal tree problem

Jayadeva

Bhaumik

1994

Biol. Cybern.

View full text Add to dashboard Cite

Abstract. The problem of finding the shortest tree connecting a set of points is called the Steiner minimal tree problem and is nearly three centuries old. It has applications in transportation, computer networks, agriculture, telephony, building layout and very large scale integrated circuit (VLSI) design, among others, and is known to be NP-complete. We propose a neural network which selforganizes to find a minimal tree. Solutions found by the network compare favourably with the best known or optimal results on test problems from the literature. To the best of our knowledge, the proposed network is the first neural-based solution to the problem. We show that the neural network has a built-in mechanism to escape local minima.

show abstract

Set of test problems for the minimum length connection networks

Cited by 14 publications

References 2 publications

Minimum Steiner trees, roots of a polynomial, and other magic

Minimum Steiner trees, roots of a polynomial, and other magic

An improved algorithm for computing Steiner minimal trees in Euclidean d-space

A neural network for the Steiner minimal tree problem

Contact Info

Product

Resources

About