Identify aproject type that generates substantial new revenue or profits for the firm.

Given a set of points in Euclidean space, which are being clustered using the K-means algorithm with Euclidean distance, the triangle inequality can be used in the assignment step to avoid calculating all the distances of each point to each cluster centroid. Provide a general discussion of how this might work.

Charles Elkan presented the following theorem in his keynote speech at the Workshop on Clustering High-Dimensional Data at SIAM 2004. Lemma 1:Let x be a point, and let b and c be centers. If d(b, c) ? 2d(x, b) then d(x, c) ? d(x, b).

Consider a quorum consensus protocol in which an item is stored as n replicas, and the size of read and write quorums are p and q respectively.

a. What is the maximum number of replica sites that can fail and still have the protocol work correctly? b. What is the minimum value that p and q can have such that p = q? c. Select p and q so that the maximum number of replica sites can fail and still have the protocol work correctly. For this selection, how many sites can fail?