On the best choice of a branching variable in the subset sum problem
-
Roman M. Kolpakov
and
Mikhail A. Posypkin
Abstract
The paper is concerned with estimating the computational complexity of the branch-and-bound method for the subset sum problem. We study the relationship between the way of decomposition of subproblems and the number of the method steps. The standard variant of the branch-and-bound method for the subset sum problem with binary branching is considered: any subproblem is decomposed into two more simple subproblems by assigning values 0 and 1 to a selected branching variable. It is shown that for any set of parameters of the problem the procedure of branching variables selection in the descending order of their weights is optimal.
Originally published in Diskretnaya Matematika (2017) 29, №1, 10–16 (in Russian).
Funding source: Russian Foundation for Basic Research
Award Identifier / Grant number: 15-07-03102A
Funding statement: This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 15-07-03102A) and the Programme of the President of the Russian Federation for the Support of Leading Scientific Schools (grant no. NSh-8860.2016.1).
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Solving systems of linear Boolean equations with noisy right-hand sides over the reals
- Reduced multitype critical branching processes in random environment
- On automorphisms of a distance-regular graph with intersection array {99, 84, 30; 1, 6, 54}
- On the best choice of a branching variable in the subset sum problem
- On periodic properties of polylinear shift registers
- Upper estimate of a combinatorial sum
Articles in the same Issue
- Frontmatter
- Solving systems of linear Boolean equations with noisy right-hand sides over the reals
- Reduced multitype critical branching processes in random environment
- On automorphisms of a distance-regular graph with intersection array {99, 84, 30; 1, 6, 54}
- On the best choice of a branching variable in the subset sum problem
- On periodic properties of polylinear shift registers
- Upper estimate of a combinatorial sum
