Question: Prove that the knapsack problem is in NP To show a problem belongs to NP, you must do four things: 1) describe the encoding used

Prove that the knapsack problem is in NP Prove that the knapsack problem is in NP To show a
To show a problem belongs to NP, you must do four things:
1) describe the encoding used for the instance
2) describe the encoding used for the certificate
3) describe the algorithm that will check if the certificate is a valid solution
4) analyze the time complexity of that algorithm.
If the complexity is bounded by some polynomial of the input size, then the problem is indeed in NP

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

Q:

Roger is a SES Officer for the Department of the Army. On 4 January, his financial adviser sold $1,001 worth of his BigCo stock and purchased $1,001 worth of SmallCo stock based on some insight he...

Q:

Prove that the Knapsack Problem (Problem 13.4, Page 550) is in NP. See Example 13.1 (Page 556) for the (partial) solution to a similar problem. [It would be a complete (rather than partial) solution...

Q:

Prove that the Knapsack Problem (Problem 13.4, Page 550) is in NP. See Example 13.1 (Page 556) for the (partial) solution to a similar problem. [It would be a complete (rather than partial) solution...

Q:

Show that the Clique Problem (Problem 13.11,) belongs to NP. To show a problem belongs to NP, you must do four things: 1) describe the encoding used for the instance 2) describe the encoding used for...

Q:

In this question you will be asked to reflect on a project you have been involved in or observed, in which a design evolved, or could have evolved, through applying a theory of user behaviour. You...

Q:

Consider the trigonometric series a0 2 + X r=1 (ar cos rx + br sin rx) where a0, a1, a2, . . . and b1, b2, . . . are constants and suppose that f(x) is a periodic function of x with period 2. (a)...

Q:

In a Hopfield neural network configured as an associative memory, with all of its weights trained and fixed, what three possible behaviours may occur over time in configuration space as the net...

Q:

Jupyter Notebook Now that we have tried our hand at some single-layer nets, let's see how they stack up compared to multi-layer nets. :) We will be exploring the basic concepts of learning non-linear...

Q:

ANSI-SPARC6 Programming Language Compilation Write notes on each of the following topics: (a) the implementation of labels and jumps in a recursive, block structured programming language [7 marks]...

Q:

Let i and j be positive integers. (i) Prove that there exist natural numbers a and b such that ai = bj+gcd(i, j). You may use standard results provided that you state them clearly. [4 marks] (ii) Let...

Q:

Consider the straightforward (nonpolynomial-time) reduction in the proof of Theorem 34.9. Describe a circuit of size n that, when converted to a formula by this method, yields a formula whose size is...

Q:

When is revenue recognized?

Q:

What impacts does currency fluctuations have on trade?

Q:

Create a spreadsheet that includes five ( 5 ) common short - term financial goals, five ( 5 ) common medium - term financial goals, and five ( 5 ) common long - term financial goals.

Q:

Compared with half a century ago, adoption has become _ _ _ _ _ _ _ _ _ common, but it is more open and acceptabl e , so we probably discuss it _ _ _ _ _ _ _ . fill in the blanks more or much less or...

Q:

How many Tables Will Base HCMSs typically have? Why?

Q:

What is the process of normalization?

Q:

What is Notation in Data Modeling, and what is the most common Notation Type used?