Succinct enumeration of distant vertex pairs

2019 ◽  
Vol 11 (06) ◽  
pp. 1950076
Author(s):  
Ali Gholami Rudi
Keyword(s):  
Shortest Paths ◽  
Graph Diameter ◽  
All Pairs Shortest Paths ◽  
Memory Complexity ◽  
General Graphs ◽  
Memory Constraints

The fastest known algorithms for finding the exact value of the diameter of general graphs are no faster than the algorithms that compute all-pairs shortest paths. An extension of the problem of computing graph diameter is enumerating pairs of vertices in a graph, ordered decreasingly by their distance. In this paper, we investigate this problem with the presence of memory constraints. We also show how our result can help the computation of graph Hyperbolicity, by lowering the memory complexity of computing the ordered list of far-apart vertex pairs.

scholarly journals Computing All-Pairs Shortest Paths by Leveraging Low Treewidth

2012 ◽  
Vol 43 ◽  
pp. 353-388 ◽  
Author(s):  
L. R. Planken ◽  
M. M. De Weerdt ◽  
R. P.J. Van der Krogt
Keyword(s):  
Directed Graphs ◽  
Shortest Paths ◽  
Efficient Algorithms ◽  
Chordal Graphs ◽  
Directed Path ◽  
All Pairs Shortest Paths ◽  
Vertex Ordering ◽  
Graph Separators ◽  
Run Time ◽  
General Graphs

We present two new and efficient algorithms for computing all-pairs shortest paths. The algorithms operate on directed graphs with real (possibly negative) weights. They make use of directed path consistency along a vertex ordering d. Both algorithms run in O(n^2 w_d) time, where w_d is the graph width induced by this vertex ordering. For graphs of constant treewidth, this yields O(n^2) time, which is optimal. On chordal graphs, the algorithms run in O(nm) time. In addition, we present a variant that exploits graph separators to arrive at a run time of O(n w_d^2 + n^2 s_d) on general graphs, where s_d

scholarly journals Average update times for fully-dynamic all-pairs shortest paths

2011 ◽  
Vol 159 (16) ◽  
pp. 1751-1758
Author(s):  
Tobias Friedrich ◽  
Nils Hebbinghaus
Keyword(s):  
Shortest Paths ◽  
All Pairs Shortest Paths

A Near-Optimal Offline Algorithm for Dynamic All-Pairs Shortest Paths in Planar Digraphs

2022 ◽  
pp. 3482-3495
Author(s):  
Debarati Das ◽  
Maximilian Probst Gutenberg ◽  
Christian Wulff-Nilsen
Keyword(s):  
Shortest Paths ◽  
All Pairs Shortest Paths
Sign in / Sign up

Export Citation Format

Share Document