Note that a mixing strategy can be described by a bipartite graph with the left-side vertices corresponding to the coins and the right-side vertices corresponding to the transactions, and there is an...

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Note that a mixing strategy can be described by a bipartite graph with the left-side vertices corresponding to the coins and the right-side vertices corresponding to the transactions, and there is an edge between a coin Ci and a transaction Tj if Ci is included in Tj as an input (genuine or fake). Design an algorithm of time complexity O(n+m), where n is the number of coins (or equivalently, the number of transactions) and m is the number of edges in the bipartite graph, that determines if a particular mixing is bad, i.e., a unique mapping M that maps ALL coins to their corresponding transactions could be found. The algorithm must output M if the mixing is bad. a)Describe the algorithm in plain English together with a short pseudocode. The algorithm must be described in an unambiguous and concise way and provides enough details so that another student can understand how it works and why it solves the problem. The input of the algorithm is n, m, the (adjacency) lists of transactions Li (abbreviation for “Left”) that include the coin Ci as an input, i = 1,2,...,n, and the (adjacency) lists of coins Rj (abbreviation for “Right”) that are inputs of Transaction Tj , j = 1,2,...,n. The output of the algorithm is either the unique mapping M of coins and transactions or None, which indicates that an unique mapping can’t be found, i.e., there are more than one valid mappings. c) Demonstrate your algorithm with an example, e.g., in Fig. 4 a). d)Show that the complexity is indeed in O(n + m), which means that there are constants a and b such that the complexity is at most a×n+b×m, e.g. 3n+2m.
Answered Same DayMay 31, 2022

Answer To: Note that a mixing strategy can be described by a bipartite graph with the left-side vertices...

Robert answered on May 31 2022
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