Heuristics for the central tree problem

Abstract

This paper addresses the central spanning tree problem (CTP). The problem consists in finding a spanning tree that minimizes the so-called robust deviation, i.e. deviation from a maximally distant tree. The distance between two trees is measured by means of the symmetric difference of their edge sets. The central tree problem is known to be NP-hard. We attack the problem with a hybrid heuristic consisting of: (1) a greedy construction heuristic to get a good initial solution and (2) fast local search improvement. We illustrate computationally efficiency of the proposed approach.

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

“…The author has shown the results of experiments for graphs having up to 50 nodes. For the central spanning tree problem some heuristics were proposed in Bang-Jensen and Nikulin (2010) and the computational tests were performed for graphs having up to 200 nodes. These heuristics, however, cannot be applied directly to the more general minmax regret minimum spanning tree problem.…”

“…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.…”