Graph Separators, with Applications

2002 ◽  
Keyword(s):  
Graph Separators

Graph Separators: A Parameterized View

2001 ◽  
pp. 318-327 ◽  
Author(s):  
Jochen Alber ◽  
Henning Fernau ◽  
Rolf Niedermeier
Keyword(s):  
Graph Separators

General Variable Neighborhood Search for computing graph separators

2014 ◽  
Vol 11 (6) ◽  
pp. 1069-1089 ◽  
Author(s):  
Jesús Sánchez-Oro ◽  
Nenad Mladenović ◽  
Abraham Duarte
Keyword(s):  
Variable Neighborhood Search ◽  
Neighborhood Search ◽  
Graph Separators

scholarly journals Graph separators: a parameterized view

2003 ◽  
Vol 67 (4) ◽  
pp. 808-832 ◽  
Author(s):  
Jochen Alber ◽  
Henning Fernau ◽  
Rolf Niedermeier
Keyword(s):  
Graph Separators

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

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