Polynomial Time Construction Algorithm of BCNC for Network Coding in Cyclic Networks

2009 ◽  
Author(s):  
Jiaqing Huang ◽  
Liang Wang ◽  
Wenqing Cheng ◽  
Hui Li
Keyword(s):  
Network Coding ◽  
Polynomial Time ◽  
Construction Algorithm ◽  
Cyclic Networks

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.

Polynomial-Time Construction of Linear Network Coding

2008 ◽  
pp. 271-282 ◽  
Author(s):  
Kazuo Iwama ◽  
Harumichi Nishimura ◽  
Mike Paterson ◽  
Rudy Raymond ◽  
Shigeru Yamashita
Keyword(s):  
Network Coding ◽  
Polynomial Time ◽  
Linear Network ◽  
Linear Network Coding
Sign in / Sign up

Export Citation Format

Share Document