Consider the following problem: Long Enough Cycle Input: undirected simple graph G = (V, E) with |V| = n, positive integer k Question: Does G contain a simple cycle containing at least k vertices? a) Describe the language Llong for Long Enough Cycle. b) Show that Long Enough Cycle is in NP. Hint for b): Give a polynomial verifier Viong for Ltong Explain why Viong satisfies the definition of verifier and why it is is indeed a polynomial time verifier. Don't forget to describe what a certificate looks like.

Consider the following problem: Long Enough Cycle Input: undirected simple graph G = (V, E) with |V| = n, positive integer k Question: Does G contain a simple cycle containing at least k vertices? a) Describe the language Llong for Long Enough Cycle. b) Show that Long Enough Cycle is in NP. Hint for b): Give a polynomial verifier Viong for Ltong Explain why Viong satisfies the definition of verifier and why it is is indeed a polynomial time verifier. Don't forget to describe what a certificate looks like.

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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Consider the following graph and a heuristic fucntion h. Please check if h is admissible
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Can you help me solve this exercise? Please note that the greedy approach described in the advice paragraph does not work.
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