Square-root sum problem

The square-root sum problem is a computational problem from the field of numerical analysis.

Details

It is defined as follows:^[1]

Given n positive integers $a_{1},\ldots ,a_{n}$ and an integer k, decide whether $\sum _{i=1}^{n}a_{i}\leq k$ .

The problem can be solved in polynomial time in the Real RAM model.^[2] However, its run-time complexity in the Turing machine model is open, as of 1999.^[1]

References

^ ^a ^b Goemans, Michel X. (1997-10-01). "Semidefinite programming in combinatorial optimization". Mathematical Programming. 79 (1): 143–161. doi:10.1007/BF02614315. ISSN 1436-4646.
^ Tiwari, Prasoon (1992-12-01). "A problem that is easier to solve on the unit-cost algebraic RAM". Journal of Complexity. 8 (4): 393–397. doi:10.1016/0885-064X(92)90003-T. ISSN 0885-064X.

[:0-1] Goemans, Michel X. (1997-10-01). "Semidefinite programming in combinatorial optimization". Mathematical Programming. 79 (1): 143–161. doi:10.1007/BF02614315. ISSN 1436-4646.

[2] Tiwari, Prasoon (1992-12-01). "A problem that is easier to solve on the unit-cost algebraic RAM". Journal of Complexity. 8 (4): 393–397. doi:10.1016/0885-064X(92)90003-T. ISSN 0885-064X.

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