(V, E), does G contain a path that One-Tenth-Path Problem: Given an undirected graph G = passes through at least one tenth of the vertices in G?

Cook's theorem proved the first NP-hard and first NP-complete problem which is the problem. C-SAT Clique halting traveling salesperson

Given a 3-CNF formula and number k find if there exists a satisfying assignment such that at least kvariables are FALSE. Is this problem NP-complete or not? Why?

Give a) an example of a valid instance of the summation problem that is not a valid instance of the minimum problem, and b) vice-versa. Write the problem definition for each of these problems.

The Study of Computers In every node of a left-child, right-sibling tree T with n nodes, there is a score that is a positive real number greater than 0. Find a subset S of all the nodes that maximises the total of their scores while guaranteeing that neither the parent node nor the child node may be in S. 1. Create a function in C++ that can solve the maximum sum for nodes using the conditions that are specified. 2. Determine the running time

L = {f in SAT | the number of satisfying assignments of f > 1/2 |f| } Show that L is NP-complete

[Introduction to the Design and Analysis of Algorithms, 3rd Edition] Maxima search. A point (xi, yi) in the Cartesian plane is said to be dominated by point (xj , yj ) if xi ≤ xj and yi ≤ yj with at least one of the two inequalities being strict. Given a set of n points, one of them is said to be a maximum of the set if it is not dominated by any other point in the set. For example, in the figure below, all the maximum points of the set are circled. Design an efficient algorithm for finding all the maximum points of a given set of n points in the Cartesian plane. What is the time efficiency class of your algorithm?

Solve the following exercise using jupyter notebook for Python, to find the objective function, variables, constraint matrix and print the graph with the optimal solution. Use linear programming methods to solve this problem. Represent the constraints and the objective function mathematically in code. Use Python and the SciPy and Matplotlib libraries to solve the problem and visualize the optimal solution on a graph. Clearly state the optimal solution and any assumptions made while solving the problem.   A farm specializes in the production of a special cattle feed, which is a mixture of corn and soybeans. The nutritional composition of these ingredients and their costs are as follows: - Corn contains 0.09 g of protein and 0.02 g of fiber per gram, with a cost of.$0.30 per gram.- Soybeans contain 0.60 g of protein and 0.06 g of fiber per gram, at a cost of $0.90 per gram.0.90 per gram. The dietary needs of the specialty food require a minimum of 30% protein and a maximum of 5% fiber.…

Prove this issue is NP-complete:   S and t are integer integers. Does S have a subset with a t-sum?   Data Structures and Algorithm issue

Demonstrate that the following issue falls within the NP class: A set S of integers and an integer number t are provided to us. Exists a subset of S such that the product of its components equals t? Note: Problem with Data Structures and Algorithms