Consider a multi-robot task assignment problem where N robots are assigned to perform M tasks with N ≥ M. Each robot must perform one task. Each task can be performed by more than one robot. Design a strategy to find all possible feasible assignments. (Hint: Set partition1 + permutation)

Classify the 1’s, 2’s, 3’s for the zip code data in R. (a) Use the k-nearest neighbor classification with k = 1, 3, 5, 7, 15. Report both the training and test errors for each choice. (b) Implement the LDA method and report its training and testing errors. Note: Before carrying out the LDA analysis, consider deleting variable 16 first from the data, since it takes constant values and may cause the singularity of the covariance matrix. In general, a constant variable does not have a discriminating power to separate two classes.

1. Let S = {1,2...n} be a set activities, where activity i € S has a start time si, a finish time f; and a profit p, asSociated with it. Design an dynamic programming algorithm for computing a set of compatible activities of maximum profit. Argue that the time complexity of you algorithm is O(n log(n)). (You must start with the correct definitions, and then write a recurrence relation.)

2. Assume an interaction matrix with a minimum of 12 nodes. Demonstrate how the Kruskal algorithm can produce better results using the parallel approach.