Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 29, Problem 3P
(a)
Program Plan Intro
To determine that weak duality holds for integer linear
(b)
Program Plan Intro
To show duality does not always holds good for integer linear program.
(c)
Program Plan Intro
To show primal integer program and dual integer program are feasible and bounded
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Show that the following problem belongs to NP class:
we are given a set S of integer numbers and an integer number t. Does S have a subset such that sum of its elements is t?
Note: Data Structures and Algorithm problem
Theorem to prove:
Any NP-complete issue that can be solved in polynomial time is P D NP. In other words, if any NP problem is not solvable in polynomial time, then no NP-complete problem is solvable in polynomial time.
Interpret the statement “If a problem A is NP-Complete, there exists a non-deterministic polynomial time algorithm to solve A”. Discuss the non-deterministic polynomial time algorithm with an example.
Chapter 29 Solutions
Introduction to Algorithms
Ch. 29.1 - Prob. 1ECh. 29.1 - Prob. 2ECh. 29.1 - Prob. 3ECh. 29.1 - Prob. 4ECh. 29.1 - Prob. 5ECh. 29.1 - Prob. 6ECh. 29.1 - Prob. 7ECh. 29.1 - Prob. 8ECh. 29.1 - Prob. 9ECh. 29.2 - Prob. 1E
Ch. 29.2 - Prob. 2ECh. 29.2 - Prob. 3ECh. 29.2 - Prob. 4ECh. 29.2 - Prob. 5ECh. 29.2 - Prob. 6ECh. 29.2 - Prob. 7ECh. 29.3 - Prob. 1ECh. 29.3 - Prob. 2ECh. 29.3 - Prob. 3ECh. 29.3 - Prob. 4ECh. 29.3 - Prob. 5ECh. 29.3 - Prob. 6ECh. 29.3 - Prob. 7ECh. 29.3 - Prob. 8ECh. 29.4 - Prob. 1ECh. 29.4 - Prob. 2ECh. 29.4 - Prob. 3ECh. 29.4 - Prob. 4ECh. 29.4 - Prob. 5ECh. 29.4 - Prob. 6ECh. 29.5 - Prob. 1ECh. 29.5 - Prob. 2ECh. 29.5 - Prob. 3ECh. 29.5 - Prob. 4ECh. 29.5 - Prob. 5ECh. 29.5 - Prob. 6ECh. 29.5 - Prob. 7ECh. 29.5 - Prob. 8ECh. 29.5 - Prob. 9ECh. 29 - Prob. 1PCh. 29 - Prob. 2PCh. 29 - Prob. 3PCh. 29 - Prob. 4PCh. 29 - Prob. 5P
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- Which of the following is NOT enough to show that a problem P is NP-Hard? Reduce the traveling salesperson problem to P in polynomial time Reduce every NP problem to P in polynomial time reducing the C-SAT problem to p in polynomial time Reduce the 01-knapsack problem to P in polynomial timearrow_forwardAlgorithm HILBERT–HURWITZGiven a rational plane curve C, the algorithm computes an (algebraically) optimal parametrization of the curve C.arrow_forwardAlgorithm OPTIMAL-PARAMETRIZATION.Given F(x, y, z) ∈ Q[x, y, z], an irreducible homogeneous polynomial defining a rational plane curve C, the algorithm computes an optimal rational parametrization of Carrow_forward
- A graduate student is working on a problem X. After working on it for several days she is unable to find a polynomial-time solution to the problem. Therefore, she attempts to prove that he problem is NP-complete. To prove that X is NP-complete she first designs a decision version of the problem. She then proves that the decision version is in NP. Next, she chooses SUBSET-SUM, a well-known NP-complete problem and reduces her problem to SUBSET-SUM (i.e., she proves X £p SUBSET-SUM). Is her approach correct? Explain your answer.arrow_forwardGiven a problem X and Y, if X reduces to Y in polynomial time, and Y is known to be NP-Complete, what can be said about X?arrow_forwardfirst describe how to test whether a linear program is feasible, and if it is, how to produce a slack form for which the basic solution is feasible. We conclude by proving the fundamental theorem of linear programming, which says that the SIMPLEX procedure always produces the correct resultarrow_forward
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