Distance Approximating Trees in Graphs

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Presentation transcript:

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) if for any

Distance Approximating Trees in Graphs Distance -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.