Partial inverse maximum spanning tree in which weight can only be decreased under \(l_p\)-norm
- 58 Downloads
The maximum or minimum spanning tree problem is a classical combinatorial optimization problem. In this paper, we consider the partial inverse maximum spanning tree problem in which the weight function can only be decreased. Given a graph, an acyclic edge set, and an edge weight function, the goal of this problem is to decrease weights as little as possible such that there exists with respect to function containing the given edge set. If the given edge set has at least two edges, we show that this problem is APX-Hard. If the given edge set contains only one edge, we present a polynomial time algorithm.
KeywordsPartial inverse problem Spanning tree Polynomial time algorithm Computational complexity
This research is supported by NSFC (Nos. 11571155, 11531011, and 61222201) and the Fundamental Research Funds for the Central Universities (Nos. lzujbky-2017-163 and lzujbky-2016-102).
- 3.Burton, D., Toint, Ph.L.: On an instance of the inverse shortest paths problem. Math. Progr. 53(1), 45–61 (1992)Google Scholar
- 8.Demange, M., Monnot, J.: An introductuion to inverse combinatorial problems. In: Paschos, V.Th (ed.) Paradigms of Combinatorial Optimization, 2nd edn. Wliey, Hoboken (2014)Google Scholar
- 12.Lai, T., Orlin, J.: The complexity of preprocessing. Research Report of Sloan School of Management, MIT (2003)Google Scholar
- 14.Orlin, J. B.: Max flows in \(O(nm)\) time, or better. In: Proceedings of the forty-fifth annual ACM Symposium on Theory of Computing (STOC 2013), 765–774 (2013)Google Scholar