An exact algorithm for the Maximum Leaf Spanning Tree problem

Regenerator location problem: Polyhedral study and effective branch-and-cut algorithms

“…Fan and Watson (2012) presented compact formulations for the MCDSP and solved these formulations using CPLEX 12.1. Fernau et al (2011) developed an exact approach, which can solve the MCDSP in O (1.8966 n ) time, but did not present computational results. Gendron et al (2014) investigated further the branch-and-cut algorithm developed by Simonetti et al (2011) , and presented a Benders decomposition algorithm, a branch-and-cut method and a hybrid algorithm combining these two algorithms.…”

An exact exponential-time algorithm for the Directed Maximum Leaf Spanning Tree problem

“…As exemplified by [2,3], it is not necessarily the case that a direct analysis (not using the parameterized detour) always produces better running time upper-bounds. However, this is the case with our problem: Our algorithm (inspired by the one of [11]) achieves a running time of O * (1.9044 n ). Notice that the algorithm of [11] is not trivially transferrable to the directed version.…”

“…However, this is the case with our problem: Our algorithm (inspired by the one of [11]) achieves a running time of O * (1.9044 n ). Notice that the algorithm of [11] is not trivially transferrable to the directed version.…”

“…A crucial ingredient of the algorithm was also to create floating leaves, i.e., vertices which are final leaves in the future solution but yet not attached to T , the tree which is grown. This concept has been already used in [11] and partly by [8]. In the undirected case we guarantee that in the bottleneck case we can generate at least two such leaves.…”

“…Several exact exponential-time algorithms have been reported in the undirected case, where the problem is also known as Connected Dominating Set, see [11,13,23]. The best run times make again use of variants of the algorithm of J. Kneis, A. Langer and P. Rossmanith [16].…”