The subset sum problem is defined as follows:SUBSETSUM = {(a1, a2,...,am; b) : m,a1, a2, ...,am; b are integers and3IC {1,2, ..., m} such that Eier a; =b}.Assume you have a polynomial-time algorithm A that decides, for any input sequence(a1, a2, ...,am, b), whether or not (a1, a2, ...,am, b) E SUBSETSUM. Note that this algorithmonly returns YES or NO; it does not return anything else.Design a polynomial-time algorithm B that takes an arbitrary sequence (a1, az, ..., am, b)as input.• If (a1, a2, ...,am; b) E SUBSETSUM, then B returns a subset I of {1,2, ..., m} suchthat Eier a; = b.If (a1, a2, ..., am, b) & SUBSETSUM, then B returns NO.Your algorithm B may use algorithm A as a black box. As always, justify your answer.

Tо sоlve the рrоblem in Рseudо-роlynоmiаl time use the Dynаmiс рrоgrаmming.Sо we will…

Answered: The subset sum problem is defined as…

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...

See similar textbooks

Similar questions

refer to image
Recall a set A is countable if |N| ≥ |A|. Recall that Cantor’s theorem shows that P(N) = {X ⊆ N}is uncountable. We will show that F = {X ⊆ N | |X| < ∞} is countable, with an onto functiong : N → F that is computable.Write a program/function (e.g., in Python) that runs forever and prints every element of F,e.g., if run it would print something like{0}{1}{0,2}{3}{0,2}{0,5,7}{1}{0,1}{}{2}...(Note that you must prove that the program works, i.e., it prints every element of F, and onlyelements of F.)
There are n people who want to carpool during m days. On day i, some subset si ofpeople want to carpool, and the driver di must be selected from si . Each person j hasa limited number of days fj they are willing to drive. Give an algorithm to find a driverassignment di ∈ si each day i such that no person j has to drive more than their limit fj. (The algorithm should output “no” if there is no such assignment.) Hint: Use networkflow.For example, for the following input with n = 3 and m = 3, the algorithm could assignTom to Day 1 and Day 2, and Mark to Day 3. Person Day 1 Day 2 Day 3 Limit 1 (Tom) x x x 2 2 (Mark) x x 1 3 (Fred) x x 0
Input: An odd integer B, and a set A= {a_1, . .. , a_2n} of 2n distinct positive integers. Question: Decide whether A can be partitioned inton disjoint pairs (a_i, a_j), where 1 s i
5. You are given a set of n positive numbers A = {a₁,..., an} and a positive integer t. Design a dynamic programming algorithm running in O(nt) time that decides whether there exists a subset A' CA such that Σ x = t. Note that each element of A can be xЄA' used at most once. Is the run-time of your algorithm polynomial with respect to the size of the input?
If you are given a set S of integers and a number t, prove that this issue falls into the NP class. Is there a subset of S where the total number of items is t? Note: Complexity in Data Structures and Algorithms
Let A = {(N1, N2) | N1 and N2 are NFAS and L(N1)N L(N2) = Ø}. Show that A is decidable.
Let S be a set of n distinct positive integers, where n is odd. The median of S is the (n+1)/2th smallest number of this set - i.e., the number in the middle of the set once the set is sorted. For example, if S = [70, 10, 20, 60, 30], then the sorted set is [10, 20, 30, 60, 70], from which we see that the median is 30. There is an obvious linearithmic algorithm to determine the median of S. First you sort the set, which takes O(n log n) time. Then you output the value of S[(n+1)/2}, which takes O(1) time. But is this the best we can do? Here is a bold claim: there is an O(n) algorithm to determine the median of set S. Determine whether the above claim is TRUE or FALSE.

Recommended textbooks for you

Computer Networking: A Top-Down Approach (7th Edi…

Computer Engineering

ISBN:

9780133594140

Author:

James Kurose, Keith Ross

Publisher:

PEARSON

Computer Organization and Design MIPS Edition, Fi…

Computer Engineering

ISBN:

9780124077263

Author:

David A. Patterson, John L. Hennessy

Publisher:

Elsevier Science

Network+ Guide to Networks (MindTap Course List)

Computer Engineering

ISBN:

9781337569330

Author:

Jill West, Tamara Dean, Jean Andrews

Publisher:

Cengage Learning

Computer Networking: A Top-Down Approach (7th Edi…

Computer Engineering

ISBN:

9780133594140

Author:

James Kurose, Keith Ross

Publisher:

PEARSON

Computer Organization and Design MIPS Edition, Fi…

Computer Engineering

ISBN:

9780124077263

Author:

David A. Patterson, John L. Hennessy

Publisher:

Elsevier Science

Network+ Guide to Networks (MindTap Course List)

Computer Engineering

ISBN:

9781337569330

Author:

Jill West, Tamara Dean, Jean Andrews

Publisher:

Cengage Learning

Concepts of Database Management

Computer Engineering

ISBN:

9781337093422

Author:

Joy L. Starks, Philip J. Pratt, Mary Z. Last

Publisher:

Cengage Learning

Prelude to Programming

Computer Engineering

ISBN:

9780133750423

Author:

VENIT, Stewart

Publisher:

Pearson Education

Sc Business Data Communications and Networking, T…

Computer Engineering

ISBN:

9781119368830

Author:

FITZGERALD

Publisher:

WILEY

SEE MORE TEXTBOOKS