Algorithm Problem Computer Science Data Structures and Algorithms

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Subjects -> Computer Science -> Data Structures and Algorithms -> Posting #107824

Computer Science, Data Structures and Algorithms

Year 1

Algorithm Problem

Mr. Johnson draws an n-input comparison network with m comparators according to the following conventions. The lines of the network go left-to-right, and comparators are drawn vertically to connect two lines. The network is drawn on an underlying grid, so that each comparator occupies one of at most m columns. Comparators can share columns, but they do not overlap. An example of such a drawing is given below for a 4-input sorting networks.

Mr. Johnson represents a given drawing as a list L of triples, in which each triple (x, y, c) represents a comparator connecting line x to line y in column c. For example, a representation of the sorting network above might be the list L =  (2,4,3), (1,3,2), (1,2,1), (2,3,4), (3, 4, 1). Describe an efficient algorithm to determine the depth of a comparison network, where the input is Mr. Johnson’s representation of a drawing of the network. Analyze your algorithm in terms of m and n.

See attached file for full problem description.

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By OTA: Sandeep Kumar, MTech

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