## Sum of All-Pairs Shortest Path Distances in a Planar Graph in Subquadratic Time

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**Sum of All-Pairs Shortest Path Distances in a Planar Graph in Subquadratic Time.** / Wulff-Nilsen, Christian.

Research output: Working paper › Research

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*Sum of All-Pairs Shortest Path Distances in a Planar Graph in Subquadratic Time*. (pp. 1-10).

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TY - UNPB

T1 - Sum of All-Pairs Shortest Path Distances in a Planar Graph in Subquadratic Time

AU - Wulff-Nilsen, Christian

PY - 2008

Y1 - 2008

N2 - We consider the problem of computing the Wiener index of a graph, defined as the sum of distances between all pairs of its vertices. It is an open problem whether the Wiener index of a planar graph can be found in subquadratic time. We solve this problem by presenting an algorithm with O(n^2*log log n/log n) running time and O(n) space requirement where n is the number of vertices of the graph.

AB - We consider the problem of computing the Wiener index of a graph, defined as the sum of distances between all pairs of its vertices. It is an open problem whether the Wiener index of a planar graph can be found in subquadratic time. We solve this problem by presenting an algorithm with O(n^2*log log n/log n) running time and O(n) space requirement where n is the number of vertices of the graph.

M3 - Working paper

SP - 1

EP - 10

BT - Sum of All-Pairs Shortest Path Distances in a Planar Graph in Subquadratic Time

CY - DIKU

ER -

ID: 9617991