Using the nearest-neighbor heuristic for the Euclidean Traveling Salesperson Problem guarantees that the path will not have crossing edges. O True O False

Suppose you are given a directed graph G on n vertices, each of which is assigned a colour. (In this problem, both endpoints of an edge can have the same colour.) Give an efficient algorithm to find the length of the longest monochromatic directed walk in G. (In a walk we can revisit vertices and recross edges, whereas in a path we cannot.) Your algorithm should return "undefined" if there is a directed cycle whose vertices are all the same colour.

Consider a directed graph G=(V,E) with n vertices, m edges, a starting vertex s∈V, real-valued edge lengths, and no negative cycles. Suppose you know that every shortest path in G from s to another vertex has at most k edges. How quickly can you solve the single-source shortest path problem? (Choose the strongest statement that is guaranteed to be true.) a) O(m+n) b) O(kn) c) O( km) d) O(mn)

There are many applications of Shortest Path Algorithm. Consider the problem of solving a jumbled Rubik's Cube in the fewest number of moves. I claim that this problem can be solved using a Shortest Path Algorithm. Determine whether this statement is TRUE or FALSE. NOTE: if you want to check if this statement is TRUE, think about how the Rubik's Cube Problem can be represented as a graph. What are the vertices? Which pairs of vertices are connected with edges? What is your source vertex and what is your destination vertex? How would Dijkstra's Algorithm enable you to find the optimal sequence of moves to solve a jumbled cube in the fewest number of moves?