scholarly journals On subset sum problem in branch groups

2020 ◽  
Vol Volume 12, issue 1 ◽  
Author(s):  
Andrey Nikolaev ◽  
Alexander Ushakov
Keyword(s):  
Final Version ◽  
Subset Sum Problem ◽  
Grigorchuk Group ◽  
Np Completeness ◽  
Subset Sum ◽  
Np Complete ◽  
Np Hardness

We consider a group-theoretic analogue of the classic subset sum problem. In this brief note, we show that the subset sum problem is NP-complete in the first Grigorchuk group. More generally, we show NP-hardness of that problem in weakly regular branch groups, which implies NP-completeness if the group is, in addition, contracting. Comment: v3: final version for journal of Groups, Complexity, Cryptology. arXiv admin note: text overlap with arXiv:1703.07406

scholarly journals A scalable photonic computer solving the subset sum problem

2020 ◽  
Vol 6 (5) ◽  
pp. eaay5853 ◽  
Author(s):  
Xiao-Yun Xu ◽  
Xuan-Lun Huang ◽  
Zhan-Ming Li ◽  
Jun Gao ◽  
Zhi-Qiang Jiao ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Propagation Speed ◽  
Direct Writing ◽  
Laser Direct Writing ◽  
Time Consumption ◽  
Subset Sum Problem ◽  
Complete Problem ◽  
Strong Robustness ◽  
Subset Sum ◽  
Np Complete

The subset sum problem (SSP) is a typical nondeterministic-polynomial-time (NP)–complete problem that is hard to solve efficiently in time with conventional computers. Photons have the unique features of high propagation speed, strong robustness, and low detectable energy level and therefore can be promising candidates to meet the challenge. Here, we present a scalable chip built-in photonic computer to efficiently solve the SSP. We map the problem into a three-dimensional waveguide network through a femtosecond laser direct writing technique. We show that the photons sufficiently dissipate into the networks and search for solutions in parallel. In the case of successive primes, our approach exhibits a dominant superiority in time consumption even compared with supercomputers. Our results confirm the ability of light to realize computations intractable for conventional computers, and suggest the SSP as a good benchmarking platform for the race between photonic and conventional computers on the way toward “photonic supremacy.”

scholarly journals A family of polycyclic groups over which the uniform conjugacy problem is NP-complete

2014 ◽  
Vol 24 (04) ◽  
pp. 515-530 ◽  
Author(s):  
Bren Cavallo ◽  
Delaram Kahrobaei
Keyword(s):  
Conjugacy Problem ◽  
Subset Sum Problem ◽  
Subset Sum ◽  
Np Complete ◽  
Polycyclic Groups

In this paper, we study the conjugacy problem in polycyclic groups. Our main result is that we construct polycyclic groups Gn whose conjugacy problem is at least as hard as the subset sum problem with n indeterminates. As such, the uniform conjugacy problem over the groups Gn is NP-complete where the parameters of the problem are taken in terms of n and the length of the elements given on input.

An Algorithm Using Modular Arithmetic for the Subset Sum Problem

1990 ◽  
Vol 21 (2) ◽  
pp. 1-10
Author(s):  
Toshiro Tachibana ◽  
Hideo Nakano ◽  
Yoshiro Nakanishi ◽  
Mitsuru Nakao
Keyword(s):  
Modular Arithmetic ◽  
Subset Sum Problem ◽  
Subset Sum

scholarly journals Statistical mechanics of an NP-complete problem: subset sum

2001 ◽  
Vol 34 (44) ◽  
pp. 9555-9567 ◽  
Author(s):  
Tomohiro Sasamoto ◽  
Taro Toyoizumi ◽  
Hidetoshi Nishimori
Keyword(s):  
Statistical Mechanics ◽  
Complete Problem ◽  
Subset Sum ◽  
Np Complete
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