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Genetic algorithms to balanced tree structures in graphs
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DOI：10.1016/j.swevo.2016.06.005.png)
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Given an edge-weighted graph G = (V, E) with vertex set V and edge set E, we study in this paper the following related balanced tree structure problems in G. The first problem, called Constrained Minimum Spanning Tree Problem (CMST), asks for a rooted tree Tin G that minimizes the total weight of T such that the distance between the root and any vertex v in T is at most a given constant C times the shortest distance between the two vertices in G. The Constrained Shortest Path Tree Problem (CSPT) requires a rooted tree Tin G that minimizes the maximum distance between the root and all vertices in V such that the total weight of T is at most a given constant C times the minimum tree weight in G. The third problem, called Minimum Maximum Stretch Spanning Tree (MMST), looks for a tree Tin G that minimize the maximum distance between all pairs of vertices in V. It is easy to conclude from the literatures that the above problems are NP-hard. We present efficient genetic algorithms that return (as shown by our experimental results) high quality solutions for these problems. (C) 2016 Elsevier B.V. All rights reserved.
Keyword:
Minimum Spanning Tree
Shortest Path Tree
Tree Spanner
Balanced Spanning Tree
Minimum Maximum Stretch Spanning Tree
Genetic Algorithms
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Dynamic Programming
. Richard Bellman. Princeton University Press, Princeton, N.J., 1957. xxv+ 342 pp. $6.75..png)
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