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In a country, there are N cities, and there are some undirected roads between them. For every city there is an integer value (may be positive, negative, or zero) on it. You want to know, if there exists a cycle (the cycle cannot visit a city or a road twice), and the sum of values of the cities on the cycle is equal to 0. Note, a single vertex is not a cycle. Prove this problem is NP-Complete. Use a reduction from the Hamiltonian cycle problem.  Write down the claim that the Hamiltonian cycle problem is polynomially reducible to the original problem.

In a country, there are N cities, and there are some undirected roads between them. For every city there is an integer value (may be positive, negative, or zero) on it. You want to know, if there exists a cycle (the cycle cannot visit a city or a road twice), and the sum of values of the cities on the cycle is equal to 0. Note, a single vertex is not a cycle. Prove this problem is NP-Complete. Use a reduction from the Hamiltonian cycle problem.  Write down the claim that the Hamiltonian cycle problem is polynomially reducible to the original problem.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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In a country, there are N cities, and there are some undirected roads between them. For every city there is an integer value (may be positive, negative, or zero) on it. You want to know, if there exists a cycle (the cycle cannot visit a city or a road twice), and the sum of values of the cities on the cycle is equal to 0. Note, a single vertex is not a cycle. Prove this problem is NP-Complete. Use a reduction from the Hamiltonian cycle problem. 

Write down the claim that the Hamiltonian cycle problem is polynomially reducible to the original problem.

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