Distance Approximating Trees in Graphs

A strongly chordal graph and an additive tree 3-spanner of it, produced by our algorithm. This graph has no additive tree 2-

spanner.

Distance Approximating Trees in Graphs

• Case (it is allowed to use new edges) distance -approximating trees

– A tree T=(V,E’) is a distance –approximating tree of a graph G=(V,E)

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Distance Approximating Trees in GraphsDistance -approximating trees

• Problem: Given G and integer , decide whether G has a distance -approximating tree.

• Our results ( is the length of a longest chordless simple cycle in G)

• Applications • Given a chordal graph G. After linear time preprocessing, for any two

vertices of G, the distance with an error at most 2 can be computed in only O(1) time.

• Efficient approximate solutions of several NP-complete problems related to distances.

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