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Express the following five loosely explained problems carefully in the form as used in the "Computers and Intractability". For every problem describe the best time and space complexity you are aware of for solving the problem (from scratch) along with the few words naming or explaining the method.
i) Determining the median of n = 2 k + 1 integers.
ii) Determining the 2 largest and 2 smallest of n integers.
iii) Finding that the graph is not a forest (not acyclic).
iv) Finding that the list of n numbers has no duplicates.
v) Finding that the maximum number of the edge disjoint paths between teh vertices v and w in a graph is less than k.
A city government wants to track down the people who run the small businesses and do not pay the city’s $125 business-license fee.
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Explain the data and record structures for the vertex ordering and vertex or edge colouring (or labelling) and a suitably the greedy graph search algorithm in order to solve each of the following problems in time bound indicated.
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An Ethernet MAC sub layer receives the 1510 bytes of the data from LLC layer. Explain whether the data encapsulation can be within one frame?
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Identify and explain two major initiatives undertaken by Australian government (at federal/ state/local government level) in order to introduce the online procurement technologies.
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