Loop-Star and Loop-Tree Decompositions: Analysis and Efficient Algorithms

2012 ◽  
Vol 60 (5) ◽  
pp. 2347-2356 ◽  
Author(s):  
Francesco P. Andriulli
2005 ◽  
Vol DMTCS Proceedings vol. AE,... (Proceedings) ◽  
Author(s):  
Audrey Lee ◽  
Ileana Streinu

International audience A multi-graph $G$ on n vertices is $(k,l)$-sparse if every subset of $n'≤n$ vertices spans at most $kn'-l$ edges, $0 ≤l < 2k$. $G$ is tight if, in addition, it has exactly $kn - l$ edges. We characterize $(k,l)$-sparse graphs via a family of simple, elegant and efficient algorithms called the $(k,l)$-pebble games. As applications, we use the pebble games for computing components (maximal tight subgraphs) in sparse graphs, to obtain inductive (Henneberg) constructions, and, when $l=k$, edge-disjoint tree decompositions.


2018 ◽  
Vol 12 ◽  
pp. 25-41
Author(s):  
Matthew C. FONTAINE

Among the most interesting problems in competitive programming involve maximum flows. However, efficient algorithms for solving these problems are often difficult for students to understand at an intuitive level. One reason for this difficulty may be a lack of suitable metaphors relating these algorithms to concepts that the students already understand. This paper introduces a novel maximum flow algorithm, Tidal Flow, that is designed to be intuitive to undergraduate andpre-university computer science students.


2014 ◽  
Vol 36 (5) ◽  
pp. 1047-1064 ◽  
Author(s):  
Bin LIAO ◽  
Jiong YU ◽  
Tao ZHANG ◽  
Xing-Yao YANG

2012 ◽  
Vol 35 (3) ◽  
pp. 603-615 ◽  
Author(s):  
Fa ZHANG ◽  
Antonio Fernandez Anta ◽  
Lin WANG ◽  
Chen-Ying HOU ◽  
Zhi-Yong LIU

2020 ◽  
Vol 81 (10) ◽  
pp. 1884-1895
Author(s):  
A. M. Shevchenko ◽  
G. N. Nachinkina ◽  
M. V. Gorodnova
Keyword(s):  

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