TITLE:
A Dynamic Programming Approach for the Max-Min Cycle Packing Problem in Even Graphs
AUTHORS:
Peter Recht
KEYWORDS:
Maximum Edge-Disjoint Cycle Packing, Extremal Problems in Graph Theory, Dynamic Programming, -Shortest Path Procedure
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.6 No.4,
October
28,
2016
ABSTRACT: Let be an undirected graph. The maximum cycle packing problem in G then is to find a collection of edge-disjoint cycles Ciin G such that s is maximum. In general, the maximum cycle packing problem is NP-hard. In this paper, it is shown for even graphs that if such a collection satisfies the condition that it minimizes the quantityon the set of all edge-disjoint cycle collections, then it is a maximum cycle packing. The paper shows that the determination of such a packing can be solved by a dynamic programming approach. For its solution, an-shortest path procedure on an appropriate acyclic networkis presented. It uses a particular monotonous node potential.