THREE- AND FOUR-INDEX PROBLEMS WITH NESTED STRUCTURE |
| 3 | |
| 2012 |
| scientific article | 519.852 | ||
| 163-169 | linear programming, multi-index problems, transport type problems, reducibility, flow algorithms |
| Multi-index linear programming transport type problems are considered. One of the approaches to solving such problems is to reduce them to flow algorithms. We describe a concept of this reduction which is based on correspondence between the variables of the original problem and the arcs of an auxiliary network. It was previously shown that two-nested structure of multi-index problems is a sufficient condition for reducibility. In this paper, we prove that the two-nested structure (in the framework of the reducibility concept considered) is a necessary and sufficient condition for reducibility in the cases of three- and four-index problems. |
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