In the rectilinear metric for points given below find (a) The minimum Steiner tree (bold), its length is (b) The minimum spanning tree (dashed), its length is (c) the approximation ratio of the MST heuristic in this case is (d) Approximation error in %

In the rectilinear metric for points given below find (a) The minimum Steiner tree (bold), its length is (b) The minimum spanning tree (dashed), its length is (c) the approximation ratio of the MST heuristic in this case is (d) Approximation error in %

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Concept explainers

Heuristic System

The term heuristic is derived from the Greek word heurisko, which means “I find, discover”. Heuristics can be mental shortcuts or approaches designed from previous experiences. The main aim of the heuristic approach is to find a good enough solution to solve the problem. Test and mistake, rule of thumb, or an educated estimate are all examples of heuristics. These methods are sufficient for achieving an immediate, brief aim. When a heuristic is used in practice, it works as predicted. It can, however, produce systematic errors. Trial and error is an important heuristic that may be used in a variety of situations, from cross-linking nuts and bolts to determining the values of given input variables in mathematical puzzles. Additional hypotheses, visual illustrations, simplification, and forward or backward reasoning are all common heuristics in mathematics.

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Answer the given question with a proper explanation and step-by-step solution.

In the rectilinear metric for points given below
find
(a) The minimum Steiner tree (bold), its length is
(b) The minimum spanning tree (dashed), its length is
(c) the approximation ratio of the MST heuristic in this case is
(d) Approximation error in %

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