scholarly journals Evaluating a Weighted Graph Polynomial for Graphs of Bounded Tree-Width

10.37236/153 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
S. D. Noble
Keyword(s):  
Polynomial Time ◽  
Weighted Graph ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Graph Polynomial ◽  
Tree Width

We show that for any $k$ there is a polynomial time algorithm to evaluate the weighted graph polynomial $U$ of any graph with tree-width at most $k$ at any point. For a graph with $n$ vertices, the algorithm requires $O(a_k n^{2k+3})$ arithmetical operations, where $a_k$ depends only on $k$.

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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