The maximum weight spanning star forest problem on cactus graphs

Viet Hung Nguyen 1
1 DECISION
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : A star is a graph in which some node is incident with every edge of the graph, i.e., a graph of diameter at most 2. A star forest is a graph in which each connected component is a star. Given a connected graph G in which the edges may be weighted positively. A spanning star forest of G is a subgraph of G which is a star forest spanning the nodes of G. The size of a spanning star forest F of G is defined to be the number of edges of F if G is unweighted and the total weight of all edges of F if G is weighted. We are interested in the problem of finding a Maximum Weight spanning Star Forest (MWSFP) in G. In [C. T. Nguyen, J. Shen, M. Hou, L. Sheng, W. Miller and L. Zhang, Approximating the spanning star forest problem and its applications to genomic sequence alignment, SIAM J. Comput. 38(3) (2008) 946–962], the authors introduced the MWSFP and proved its NP-hardness. They also gave a polynomial time algorithm for the MWSF problem when G is a tree. In this paper, we present a linear time algorithm that solves the MSWF problem when G is a cactus.
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Viet Hung Nguyen. The maximum weight spanning star forest problem on cactus graphs. Discrete Mathematics, Algorithms and Applications, World Scientific Publishing, 2015, 07 (02), pp.1550018. ⟨10.1142/S1793830915500184⟩. ⟨hal-01177976⟩

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