Dynamic distance hereditary graphs using split decomposition

Authors:
Emeric Gioan;Christophe Paul
Affiliations:
CNRS - LIRMM, Université de Montpellier 2, France;CNRS - LIRMM, Université de Montpellier 2, France
Venue:
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Year:
2007

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Abstract

The problem of maintaining a representation of a dynamic graph as long as a certain property is satisfied has recently been considered for a number of properties. This paper presents an optimal algorithm for this problem on vertex-dynamic connected distance hereditary graphs: both vertex insertion and deletion have complexity O(d), where d is the degree of the vertex involved in the modification. Our vertex-dynamic algorithm is competitive with the existing linear time recognition algorithms of distance hereditary graphs, and is also simpler. Besides, we get a constant time edge-dynamic recognition algorithm. To achieve this, we revisit the split decomposition by introducing graph-labelled trees. Doing so, we are also able to derive an intersection model for distance hereditary graphs, which answers an open problem.