MAD Trees and distance-hereditary graphs

Authors:
E. Dahlhaus;P. Dankelmann;W. Goddard;H. C. Swart
Affiliations:
Institute of Computer Graphics, Vienna University of Technology, Austria;School of Mathematical and Statistical Sciences, University of Natal, Durban, South Africa;Department of Computer Science, University of Natal, 4041, Durban, South Africa;School of Mathematical and Statistical Sciences, University of Natal, Durban, South Africa
Venue:
Discrete Applied Mathematics - Special issue: The second international colloquium, "journées de l'informatique messine"
Year:
2003

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Abstract

For a graph G with weight function w on the vertices, the total distance of G is the sum over all unordered pairs of vertices x and y of w(x)w(y) times the distance between x and y. A MAD tree of G is a spanning tree with minimum total distance. We develop a linear-time algorithm to find a MAD tree of a distance-hereditary graph; that is, those graphs where distances are preserved in every connected induced subgraph.