General Polynomial Time Decomposition Algorithms

2005 ◽  
pp. 308-322 ◽  
Author(s):  
Nikolas List ◽  
Hans Ulrich Simon
Keyword(s):  
Polynomial Time ◽  
Decomposition Algorithms ◽  
General Polynomial ◽  
Time Decomposition

scholarly journals Reconstruction of score sets

2014 ◽  
Vol 6 (2) ◽  
pp. 210-229
Author(s):  
Antal Iványi
Keyword(s):  
Polynomial Time ◽  
Constructive Proof ◽  
Construction Algorithm ◽  
Polynomial Time Algorithms ◽  
General Polynomial ◽  
Degree Set ◽  
New Algorithms

Abstract The score set of a tournament is defined as the set of its different outdegrees. In 1978 Reid [15] published the conjecture that for any set of nonnegative integers D there exists a tournament T whose degree set is D. Reid proved the conjecture for tournaments containing n = 1, 2, and 3 vertices. In 1986 Hager [4] published a constructive proof of the conjecture for n = 4 and 5 vertices. In 1989 Yao [18] presented an arithmetical proof of the conjecture, but general polynomial construction algorithm is not known. In [6] we described polynomial time algorithms which reconstruct the score sets containing only elements less than 7. In [5] we improved this bound to 9. In this paper we present and analyze new algorithms Hole-Map, Hole-Pairs, Hole-Max, Hole-Shift, Fill-All, Prefix-Deletion, and using them improve the above bound to 12, giving a constructive partial proof of Reid’s conjecture.

A Polynomial-Time Decomposition Algorithm for a Petri Net Based on Indexes of Places

2008 ◽  
Vol 8 (24) ◽  
pp. 4668-4673
Author(s):  
Q. Zeng ◽  
X. Hu ◽  
J. Zhu ◽  
H. Duan
Keyword(s):  
Polynomial Time ◽  
Petri Net ◽  
Decomposition Algorithm ◽  
Time Decomposition

General polynomial decomposition and the s-1-decomposition are NP-Hard

1993 ◽  
Vol 04 (02) ◽  
pp. 147-156 ◽  
Author(s):  
Matthew T. Dickerson
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Np Hard ◽  
Decomposition Problem ◽  
The Past ◽  
Polynomial Decomposition ◽  
General Polynomial ◽  
In The Wild ◽  
Univariate Polynomial

In the past few years, much work has been done on the functional decomposition of polynomials. Beginning with the first polynomial time algorithm of Kozen and Landau1 for the decomposition of a univariate polynomial in the “tame” case, significant progress has been made toward polynomial time algoithms for the more general cases: decomposition of multivariate polynomials, and decomposition in the “wild” case.2−8 However it has remained an open problem whether general multivariate decomposition is in P. In this paper, we present a basic form for the general polynomial decomposition problem which encompasses most forms of previously examined decomposition problems, and then prove that the problem is NP-Hard by proving that a sub-problem called the S-1-Decomposition problem is NP-Hard.

The 2-closure of a 32-transitive group in polynomial time

2018 ◽  
Vol 60 (2) ◽  
pp. 360-375
Author(s):  
A. V. Vasil'ev ◽  
D. V. Churikov
Keyword(s):  
Polynomial Time ◽  
Transitive Group

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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