Minimum Weakly Fundamental Cycle Bases Are Hard To Find

Algorithmica ◽  
2007 ◽  
Vol 53 (3) ◽  
pp. 402-424 ◽  
Author(s):  
Romeo Rizzi
Keyword(s):  
Fundamental Cycle ◽  
Cycle Bases

scholarly journals Mathematical models and a constructive heuristic for finding minimum fundamental cycle bases

2005 ◽  
Vol 15 (1) ◽  
pp. 15-24 ◽  
Author(s):  
Leo Liberti ◽  
Edoardo Amaldi ◽  
Francesco Maffioli ◽  
Nelson Maculan
Keyword(s):  
Linear Programming ◽  
Total Cost ◽  
Fundamental Cycle ◽  
Cycle Basis ◽  
Cpu Time ◽  
Constructive Heuristic ◽  
Cycle Bases ◽  
Time Required ◽  
Application Fields

The problem of finding a fundamental cycle basis with minimum total cost in a graph arises in many application fields. In this paper we present some integer linear programming formulations and we compare their performances, in terms of instance size, CPU time required for the solution, and quality of the associated lower bound derived by solving the corresponding continuous relaxations. Since only very small instances can be solved to optimality with these formulations and very large instances occur in a number of applications, we present a new constructive heuristic and compare it with alternative heuristics.

Lower bounds for strictly fundamental cycle bases in grid graphs

Networks ◽  
2009 ◽  
Vol 53 (2) ◽  
pp. 191-205 ◽  
Author(s):  
Ekkehard Köhler ◽  
Christian Liebchen ◽  
Gregor Wünsch ◽  
Romeo Rizzi
Keyword(s):  
Lower Bounds ◽  
Grid Graphs ◽  
Fundamental Cycle ◽  
Cycle Bases

Algorithms for finding minimum fundamental cycle bases in graphs

2004 ◽  
Vol 17 ◽  
pp. 29-33 ◽  
Author(s):  
Edoardo Amaldi ◽  
Leo Liberti ◽  
Francesco Maffioli ◽  
Nelson Maculan
Keyword(s):  
Fundamental Cycle ◽  
Cycle Bases

scholarly journals Benchmarks for Strictly Fundamental Cycle Bases

2007 ◽  
pp. 365-378 ◽  
Author(s):  
Christian Liebchen ◽  
Gregor Wünsch ◽  
Ekkehard Köhler ◽  
Alexander Reich ◽  
Romeo Rizzi
Keyword(s):  
Fundamental Cycle ◽  
Cycle Bases
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