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Abstract
The set packing problem (SPP) is a significant NP-hard combinatorial optimization problem with extensive applications. In this paper, we encode the set packing problem as the maximum weighted independent set (MWIS) problem and solve the encoded problem with an efficient algorithm designed to the MWIS problem. We compare the independent set-based method with the state-of-the-art algorithms for the set packing problem on the 64 standard benchmark instances. The experimental results show that the independent set-based method is superior to the existing algorithms in terms of the quality of the solutions and running time obtained the solutions.
Highlights
E other is that we can make full use of the minimum weighted independent solving algorithms to better solve the set packing problem
Where xi is a binary variable, indicating whether object i is in PA, xi 1 means in PA, otherwise, xi 0 means not in PA, ci is the weight of object i, and oi, j is a binary variable, indicating whether object i belongs to exclusive constraint set Oj, oi, j 1 means belonging to set Oj, oi, j 0 means not belonging to set Oj
We will report a large number of experimental results through using the introduced DLSWCC algorithm to solve the set packing problem as a minimum weighted independent set on a large number of set packing problem standard benchmarks
Summary
E other is that we can make full use of the minimum weighted independent solving algorithms to better solve the set packing problem. E correspondent conflict graph G (Vt, Eg, w) with regard to the set packing problem instance is described in Figure 1(b) where each object is represented by a vertex whose weight is equal to that of the object.
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