A polynomial time algorithm for finding finite unions of tree pattern languages

2006 ◽  
pp. 118-131 ◽  
Author(s):  
Hiroki Arimura ◽  
Takeshi Shinohara ◽  
Setsuko Otsuki
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Pattern Languages ◽  
Tree Pattern

Efficient Processing of XML Tree Pattern Queries

2006 ◽  
Vol 10 (5) ◽  
pp. 738-743 ◽  
Author(s):  
Yangjun Chen ◽  
◽  
Dunren Che ◽  
Keyword(s):  
Dynamic Programming ◽  
Polynomial Time ◽  
Main Idea ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
The Other ◽  
Tree Pattern ◽  
Efficient Processing

In this paper, we present a polynomial-time algorithm for TPQ (tree pattern queries) minimization without XML constraints involved. The main idea of the algorithm is a dynamic programming strategy to find all the matching subtrees within a TPQ. A matching subtree implies a redundancy and should be removed in such a way that the semantics of the original TPQ is not damaged. Our algorithm consists of two parts: one for subtree recognization and the other for subtree deletion. Both of them needs only O(<I>n</I>2) time, where <I>n</I> is the number of nodes in a TPQ.

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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