Approximation algorithms for three-dimensional assignment problems with triangle inequalities
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Consider the following classical formulation of the (axial) three-dimensional assignment problem (3DA) (see e.g. Balas and Saltzman (1989)). Given is a complete tripartite graph K n,n,n = (I ∪ J ∪ K, (I × J) ∪ (I × K) ∪ (J × K)), where I, J, K are disjoint sets of size n, and a cost c ijk for each triangle (i, j,k) ∈ I × J × K. The problem 3DA is to find a subset A of n triangles, A ⊆ I × J × K, such that every element of I ∪ J ∪ K occurs in exactly one triangle of A, and the total cost c(A) = ∑(i,j,k) ∈A c ijk is minimized. Some recent references to this problem are Balas and Saltzman (1989), Frieze (1974), Frieze and Yadegar (1981), Hansen and Kaufman (1973).
KeywordsFeasible Solution Approximation Algorithm Triangle Inequality Approximate Algorithm Bipartite Match Problem
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