a. Define what f(n) = O(g(n)) means. Define the complexity classes P and NP. [5 marks]...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
a. Define what f(n) = O(g(n)) means. Define the complexity classes P and NP. [5 marks] b. We proved in class that the problem CLIQUE is NP-complete by con- structing a polynomial reduction from 3SAT to CLIQUE. i Given an input formula = (PVQVR) A (PV-Q) A (-Q V R) construct a graph G that is the result of applying the reduction. [4 marks] ii In the reduction, what is the size k of the clique that G has if y is satisfiable? [2 marks] iii Does G indeed have a clique of size k (that you computed in the previous subquestion)? If yes, show it on the graph (list the nodes and edges) and explain how you can construct a satisfying assignment to from it. If G does not have a clique of size k, explain why does not have a satisfying assignment. [4 marks] a. Define what f(n) = O(g(n)) means. Define the complexity classes P and NP. [5 marks] b. We proved in class that the problem CLIQUE is NP-complete by con- structing a polynomial reduction from 3SAT to CLIQUE. i Given an input formula = (PVQVR) A (PV-Q) A (-Q V R) construct a graph G that is the result of applying the reduction. [4 marks] ii In the reduction, what is the size k of the clique that G has if y is satisfiable? [2 marks] iii Does G indeed have a clique of size k (that you computed in the previous subquestion)? If yes, show it on the graph (list the nodes and edges) and explain how you can construct a satisfying assignment to from it. If G does not have a clique of size k, explain why does not have a satisfying assignment. [4 marks]
Expert Answer:
Related Book For
Discrete and Combinatorial Mathematics An Applied Introduction
ISBN: 978-0201726343
5th edition
Authors: Ralph P. Grimaldi
Posted Date:
Students also viewed these programming questions
-
Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...
-
s1 educated (SSE) student for every three public school educated (PSE) students. Reasoning that students are not very dissimilar from threads, he suggests the following entry and exit routines be...
-
A marketing researcher wants to estimate the mean amount spent per year ($) on a web site by membership member shoppers. Suppose a random sample of 150 membership member shoppers who recently made a...
-
The Ivanpah Solar Electric Generating System is the largest solar thermal power-tower facility in the world. It collects 1321 MW of solar thermal energy to heat special collectors to 566 C. The...
-
How do the average credit scores of people living in various cities differ? The file Credit Scores contains an ordered array of the average credit scores of 2,570 American cities. a. Construct a...
-
Use the Hubble expansion relation (9.1.1), the temperature scaling relation (9.1.3), and the energy density relation before the electron-positron annihilation (9.3.6b) to show that the temperature as...
-
Bloom Corporation had the following 2010 income statement. The following accounts increased during 2010: accounts receivable $12,000; inventory $11,000; accounts payable $13,000. Prepare the cash...
-
Consider eight threads (T1-T8) that are synchronized using Semaphores. Each thread has a critical section that is constrained to execute according to the following precedence relation: T2, T3 and T4...
-
Publishing Company, Inc. ("P") is a publicly traded C corporation engaged in the publication of professional textbooks. P has 5 million shares of voting common stock outstanding. The stock is...
-
Fill in the blanks given below: Dear Kaiser, I do like to let you know the importance of tourism. Man often takes a ride (a) various types of transports (b).. having any pressing business to attend...
-
Write the expression in the form \(D \sin (\omega t+\phi)\). \(\cos \left(2 t+\frac{1}{3} \pi ight)\)
-
Solve the IVP. Do not use Laplace transformation. \(\ddot{y}+4 y=e^{t} \sin t, \quad y(0)=0, \dot{y}(0)=\frac{1}{10}\)
-
a. Express \(z_{1} / z_{2}\) in rectangular form. b. Verify that \(\left|z_{1} / z_{2} ight|=\left|z_{1} ight| /\left|z_{2} ight|\). \(\frac{\frac{1}{3}}{-2+j}\)
-
Express each complex number in its polar form. \(\sqrt{3}+j\)
-
Solve the IVP. Do not use Laplace transformation. \(\ddot{y}-y=t^{2}-\cos t, \quad y(0)=\frac{1}{2}, \dot{y}(0)=0\)
-
(a) Given a function f(x,y,z)= 3x +2y + 6z', constrained according to the relation x + y+z = B (where B is a constant), use the method of Lagrange Multipliers to find the extremum value of f (in...
-
Ann hires a nanny to watch her two children while she works at a local hospital. She pays the 19 year-old nanny $125 per week for 48 weeks during the current year. a. What is the employers portion of...
-
(a) If p, q are primitive statements, prove that (p q) (p (p q)) (p q). (b) Write the dual of the logical equivalence in part (a).
-
Let n ¥ 2. If xl is a Boolean variable for all 1 ¤ i ¤ n, prove that (X + x ++ x,) = x, I,
-
(a) Determine the chromatic polynomials for the graphs in Fig. 11.92 (b) Find x (G) for each graph. (c) If five colors are available, in how many ways can the vertices of each graph be properly...
-
When nitrogen and fluorine combine to form a molecule, the most likely chemical formula is: (a) N 3 F. (b)N 2 F. (c) NF 4 . (d) NF. (e) NF 3 .
-
In terms of the periodic table, is there an abrupt or gradual change between ionic and covalent bonds? (a) An abrupt change occurs across the metalloids. (b) Actually, any element of the periodic...
-
A substance consisting of which of the two molecules shown below should have a higher boiling point? Why? (a) the molecule on the left, SCO, because it comes later in the periodic table (b) the...
Study smarter with the SolutionInn App