scholarly journals A polynomial time algorithm for finding rational general solutions of first order autonomous ODEs

2006 ◽  
Vol 41 (7) ◽  
pp. 739-762 ◽  
Author(s):  
Ruyong Feng ◽  
Xiao-Shan Gao
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
General Solutions ◽  
First Order

scholarly journals Betweenness of partial orders

2020 ◽  
Vol 54 ◽  
pp. 7
Author(s):  
Bruno Courcelle
Keyword(s):  
Partial Order ◽  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Second Order ◽  
Partial Orders ◽  
First Order ◽  
Betweenness Relations

We construct a monadic second-order sentence that characterizes the ternary relations that are the betweenness relations of finite or infinite partial orders. We prove that no first-order sentence can do that. We characterize the partial orders that can be reconstructed from their betweenness relations. We propose a polynomial time algorithm that tests if a finite relation is the betweenness of a partial order.

Learning Importance of Preferences

10.29007/v68w ◽  
2018 ◽  
Author(s):  
Ying Zhu ◽  
Mirek Truszczynski
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Scoring Rules ◽  
Np Hard ◽  
Individual Preferences

We study the problem of learning the importance of preferences in preference profiles in two important cases: when individual preferences are aggregated by the ranked Pareto rule, and when they are aggregated by positional scoring rules. For the ranked Pareto rule, we provide a polynomial-time algorithm that finds a ranking of preferences such that the ranked profile correctly decides all the examples, whenever such a ranking exists. We also show that the problem to learn a ranking maximizing the number of correctly decided examples (also under the ranked Pareto rule) is NP-hard. We obtain similar results for the case of weighted profiles when positional scoring rules are used for aggregation.

A polynomial-time algorithm for designing FIR filters with power-of-two coefficients

2002 ◽  
Vol 50 (8) ◽  
pp. 1935-1941 ◽  
Author(s):  
Dongning Li ◽  
Yong Ching Lim ◽  
Yong Lian ◽  
Jianjian Song
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Fir Filters
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