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The subset sum problem is defined as follows: SUBSETSUM = {(a1, a2, . , am; b) : m,a1, a2, … ..,am; b are integers and 31C {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 algorithm only 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) € SUBSETSUM, then B returns a subset I of {1,2,...,m} such that 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.

The subset sum problem is defined as follows: SUBSETSUM = {(a1, a2, . , am; b) : m,a1, a2, … ..,am; b are integers and 31C {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 algorithm only 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) € SUBSETSUM, then B returns a subset I of {1,2,...,m} such that 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.

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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The subset sum problem is defined as follows: SUBSETSUM = {(a1, a2,...,am; b) : m,a1, a2, ...,am; b are integers and 3IC {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 algorithm only 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} such that 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.
Transcribed Image Text:The subset sum problem is defined as follows: SUBSETSUM = {(a1, a2,...,am; b) : m,a1, a2, ...,am; b are integers and 3IC {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 algorithm only 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} such that 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.
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