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Hi, Anyone can have any idea or specific information how to design the shortest path algorithm and also Maximum-flow problems as shown below please?

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[1] Suppose that A is a matrix where A[i,j] is the length of a shortest path between vertices i and j in an undirected, weighted graph G with n vertices (all weights are positive). Design an algorithm that takes O(n2) time to update A when an additional edge is inserted into G.

[2] Dining problem. Several families go out to dinner together. To increase their social interaction, they would like to sit at tables so that no two members of the same family are at the same table. Show how to find a seating arrangement that meets this objective (or prove that no such arrangement exists) by reducing this problem to the maximum-flow problem. Assume that there are p families and q tables; the i-th family has ai members, the j-th table has a seating capacity of bj.

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Thanks.

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[1] Suppose that A is a matrix where A[i,j] is the length of a shortest path between vertices i and j in an undirected, weighted graph G with n vertices (all weights are positive). Design an algorithm that takes O(n2) time to update A when an additional edge is inserted into G.

[2] Dining problem. Several families go out to dinner together. To increase their social interaction, they would like to sit at tables so that no two members of the same family are at the same table. Show how to find a seating arrangement that meets this objective (or prove that no such arrangement exists) by reducing this problem to the maximum-flow problem. Assume that there are p families and q tables; the i-th family has ai members, the j-th table has a seating capacity of bj.

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Thanks.

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