in pt (polynomial time) n pt within factor 2.75 m pt within factor 1.9999 n pt within factor 1.4999 olied to the traveling salesperson problem

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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Approximation Algorithms
(1) Check (circle) whichever applied to maximum independent set in graphs:
a. NP-complete
b. Solvable exactly in pt (polynomial time)
c. Approximable in pt within factor 2.75
d. Approximable in pt within factor 1.9999
e. Approximable in pt within factor 1.4999
(2) Check whichever applied to the traveling salesperson problem:
Yes
No Don't know
Yes
No Don't know
Yes
No Don't know
Yes
No Don't know
Yes
No Don't know
a. NP-complete
b. Solvable exactly in pt (polynomial time)
Yes
No Don't know
Yes
No Don't know
c. Approximable in pt within factor 2.1666
d. Approximable in pt within factor 1.9999
e. Approximable in pt within factor 1.4999
(3) Check whichever applied to the vertex cover problem (assuming P#NP):
Yes
No Don't know
Yes
No Don't know
Yes
No Don't know
No Don't know
No Don't know
Yes
a. NP-complete
Solvable exactly in pt (polynomial time)
Yes
b.
Yes
No Don't know
No Don't know
No Don't know
Yes
d. Approximable in pt within factor 2.3333
e. Approximable in pt within factor 1.0001
с.
Approximable in pt within factor 2.9999
Yes
Transcribed Image Text:Approximation Algorithms (1) Check (circle) whichever applied to maximum independent set in graphs: a. NP-complete b. Solvable exactly in pt (polynomial time) c. Approximable in pt within factor 2.75 d. Approximable in pt within factor 1.9999 e. Approximable in pt within factor 1.4999 (2) Check whichever applied to the traveling salesperson problem: Yes No Don't know Yes No Don't know Yes No Don't know Yes No Don't know Yes No Don't know a. NP-complete b. Solvable exactly in pt (polynomial time) Yes No Don't know Yes No Don't know c. Approximable in pt within factor 2.1666 d. Approximable in pt within factor 1.9999 e. Approximable in pt within factor 1.4999 (3) Check whichever applied to the vertex cover problem (assuming P#NP): Yes No Don't know Yes No Don't know Yes No Don't know No Don't know No Don't know Yes a. NP-complete Solvable exactly in pt (polynomial time) Yes b. Yes No Don't know No Don't know No Don't know Yes d. Approximable in pt within factor 2.3333 e. Approximable in pt within factor 1.0001 с. Approximable in pt within factor 2.9999 Yes
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