Solving low-density multiple subset sum problems with SVP oracle

2016 ◽  
Vol 29 (1) ◽  
pp. 228-242 ◽  
Author(s):  
Yanbin Pan ◽  
Feng Zhang
Keyword(s):  
Low Density ◽  
Subset Sum ◽  
Subset Sum Problems

Solving low-density subset sum problems

1985 ◽  
Vol 32 (1) ◽  
pp. 229-246 ◽  
Author(s):  
J. C. Lagarias ◽  
A. M. Odlyzko
Keyword(s):  
Low Density ◽  
Subset Sum ◽  
Subset Sum Problems

On generic complexity of the subset sum problem in monoids and groups of integer matrix of order two

2020 ◽  
Vol 25 (4) ◽  
pp. 10-15
Author(s):  
Alexander Nikolaevich Rybalov
Keyword(s):  
Linear Group ◽  
Modular Group ◽  
Special Linear Group ◽  
Second Order ◽  
Integer Matrix ◽  
Subset Sum ◽  
Algorithmic Problems ◽  
Almost All ◽  
Subset Sum Problems ◽  
Generic Complexity

Generic-case approach to algorithmic problems was suggested by A. Miasnikov, I. Kapovich, P. Schupp and V. Shpilrain in 2003. This approach studies behavior of an algo-rithm on typical (almost all) inputs and ignores the rest of inputs. In this paper, we prove that the subset sum problems for the monoid of integer positive unimodular matrices of the second order, the special linear group of the second order, and the modular group are generically solvable in polynomial time.

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