MIT15_053S13_iprefguide

The larger set is usually referred to as the ground

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Unformatted text preview: ger set. The larger set is usually referred to as the ground set. For example, suppose that there is a collection of n sets 51, ", 5n where for i = 1 to n 5i is a subset of the ground set {1, 2, 3, ", m}. Associated with each set 5i is a cost Ci. ⎧1 ⎪ if i ∈ S j ⎪0 ⎩ otherwise. Let aij = ⎨ ⎧1 ⎪ if set S j is selected ⎪0 ⎩ otherwise. Let x j = ⎨ The set paCking problem is the problem of selecting the maximum cost subcollection of sets, no two of which share a common element. The set Covering problem is the problem of selecting the minimum cost subcollection of sets, so that each element i E {1, 2, ", m} is in one of the sets. Maximize subject to ∑ ∑ n j =1 n cjxj a x j ≤ 1 for each i ∈{1,..., m} j =1 ij x j ∈{0,1} Minimize subject to ∑ ∑ n j =1 n Set Packing Problem for each j ∈{1,..., n}. cjxj a x j ≥ 1 for each i ∈{1,..., m} j =1 ij x j ∈{0,1} Set Covering Problem for each j ∈{1,..., n}. For example, consider the following map of t...
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This note was uploaded on 03/18/2014 for the course MGMT 15.053 taught by Professor Jamesorli during the Spring '07 term at MIT.

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