scholarly journals A polynomial time algorithm for finding the prime factors of cartesian-product graphs

1985 ◽  
Vol 12 (2) ◽  
pp. 123-138 ◽  
Author(s):  
Joan Feigenbaum ◽  
John Hershberger ◽  
Alejandro A. Schäffer
Keyword(s):  
Polynomial Time ◽  
Cartesian Product ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Product Graphs ◽  
Prime Factors ◽  
Cartesian Product Graphs

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.

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