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8. Consider the following map: a e C b O a. Explain how we can use the graph-coloring problem to color the map so that no two neighboring regions are colored the same.

8. Consider the following map: a e C b O a. Explain how we can use the graph-coloring problem to color the map so that no two neighboring regions are colored the same.

Database System Concepts
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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1.4 Fundamental Data Structures a. The problem's statement is somewhat vague, which is typical of real-life problems. In particular, what reasonable criterion can be used for defining the "best" route? b. How would you model this problem by a graph? 7. a. Rephrase the traveling-salesman problem in combinatorial object terms. b. Rephrase the graph-coloring problem in combinatorial object terms. 8. Consider the following map: a e с b 25 d a. Explain how we can use the graph-coloring problem to color the map so that no two neighboring regions are colored the same. b. Use your answer to part (a) to color the map with the smallest number of colors. 9. Design an algorithm for the following problem: Given a set of n points in the Cartesian plane, determine whether all of them lie on the same circumference. D. Write a program that reads as its inputs the (x, y) coordinates of the endpoints of two line segments P₁Q1 and P2Q2 and determines whether the segments have a common point. undamental Data Structures nce the vast majority of algorithms of interest operate on data, particular ways of ganizing data play a critical role in the design and analysis of algorithms. A data ructure can be defined as a particular scheme of organizing related data items. e nature of the data items is dictated by the problem at hand; they can range m elementary data types (e.g., integers or characters) to data structures (e.g., a e-dimensional array of one-dimensional arrays is often used for implementing
Transcribed Image Text:1.4 Fundamental Data Structures a. The problem's statement is somewhat vague, which is typical of real-life problems. In particular, what reasonable criterion can be used for defining the "best" route? b. How would you model this problem by a graph? 7. a. Rephrase the traveling-salesman problem in combinatorial object terms. b. Rephrase the graph-coloring problem in combinatorial object terms. 8. Consider the following map: a e с b 25 d a. Explain how we can use the graph-coloring problem to color the map so that no two neighboring regions are colored the same. b. Use your answer to part (a) to color the map with the smallest number of colors. 9. Design an algorithm for the following problem: Given a set of n points in the Cartesian plane, determine whether all of them lie on the same circumference. D. Write a program that reads as its inputs the (x, y) coordinates of the endpoints of two line segments P₁Q1 and P2Q2 and determines whether the segments have a common point. undamental Data Structures nce the vast majority of algorithms of interest operate on data, particular ways of ganizing data play a critical role in the design and analysis of algorithms. A data ructure can be defined as a particular scheme of organizing related data items. e nature of the data items is dictated by the problem at hand; they can range m elementary data types (e.g., integers or characters) to data structures (e.g., a e-dimensional array of one-dimensional arrays is often used for implementing
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