On central spanning trees of a graph

A tabu search algorithm for the minmax regret minimum spanning tree problem with interval data

“…All the cost intervals are [0, 1]. The graphs of this type appear in papers (Averbakh and Lebedev 2004;Bezrukov et al 1995), where the complexity of the robust spanning tree problem was investigated. We have also tested the graphs with different proportions of the nodes in layers 1 and 2 and different number of edges linking these two layers.…”

“…It was proven in Bezrukov et al (1995) that the central spanning tree problem is strongly NP-hard. We now show, following (Aron and van Hentenryck 2004), that this problem is a special case of the minmax regret minimum spanning tree.…”

“…The central spanning tree problem has been discussed in Amoia and Cottafava (1971), Bezrukov et al (1995), Deo (1966), Bang-Jensen and Nikulin (2010) and it has some applications, for example, in the analysis of transportation networks. It was proven in Bezrukov et al (1995) that the central spanning tree problem is strongly NP-hard.…”

Heuristics for the central tree problem

“…So, for a long time, there was a hope to find an efficient algorithm for the CTP. But there was no progress in the area until the result of Bezrukov et al (1996), which states that the CTP is NP-hard. To prove that fact the authors used a transformation from Exact Cover by 3-set problem, which is known to be NPComplete (Garey and Johnson 1979).…”

“…It was also proven that the RSTP is at least as hard as central tree problem, and therefore NP-hard (Bezrukov et al 1996). These results shed a new light on the algorithms that have been proposed for RSTP, since they have focused almost exclusively on the cost structure and have ignored the topological properties of the graph.…”