On the Complexity of the Problem of Solving Systems of Tropical Polynomial Equations of Degree Two Full article
| Conference |
XXIII International Conference Mathematical Optimization Theory and Operations Research 30 Jun - 6 Jul 2024 , Омск |
||
|---|---|---|---|
| Source | Mathematical Optimization Theory and Operations Research: Recent Trends Compilation, Springer. 2024. 388 c. ISBN 978-3-031-73364-2. |
||
| Journal |
Communications in Computer and Information Science
ISSN: 1865-0929 |
||
| Output data | Year: 2024, Volume: 2239, Pages: 73–84 Pages count : 11 DOI: 10.1007/978-3-031-73365-9_5 | ||
| Tags | Tropical algebra · NP-completeness · Generic-case complexity · Asymptotic density | ||
| Authors |
|
||
| Affiliations |
|
Funding (1)
| 1 | Омский филиал ФГБУН «Институт математики им. С.Л. Соболева СО РАН». | FWNF-2022-0003 |
Abstract:
In this paper, we investigate the computational complexity of the problem of solving a one-sided system of equations of degree two of a special form over the max-plus algebra. Also, we consider the asymptotic density of solvable systems of this form. Such systems have appeared during the analysis of some tropical cryptography protocols that were recently suggested. We show how this problem is related to the integer linear programming problem and prove that this problem is NP-complete. We show that the asymptotic density of solvable systems of this form with some restrictions on the coefficients, the number of variables, and the number of equations is 0. As a corollary, we prove that this problem (with some restrictions on the coefficients, the number of variables, and the number of equations) is decidable generically in polynomial time.
Cite:
Buchinskiy I.M.
, Kotov M.V.
, Treier A.V.
On the Complexity of the Problem of Solving Systems of Tropical Polynomial Equations of Degree Two
In compilation Mathematical Optimization Theory and Operations Research: Recent Trends. – Springer., 2024. – Т.2239. – C.73–84. – ISBN 978-3-031-73364-2. DOI: 10.1007/978-3-031-73365-9_5 Scopus OpenAlex
On the Complexity of the Problem of Solving Systems of Tropical Polynomial Equations of Degree Two
In compilation Mathematical Optimization Theory and Operations Research: Recent Trends. – Springer., 2024. – Т.2239. – C.73–84. – ISBN 978-3-031-73364-2. DOI: 10.1007/978-3-031-73365-9_5 Scopus OpenAlex
Dates:
| Published print: | Dec 20, 2024 |
| Published online: | Dec 20, 2024 |
Identifiers:
| Scopus: | 2-s2.0-85214256273 |
| OpenAlex: | W4405597819 |