Source location problems considering vertex-connectivity and edge-connectivity simultaneously

Networks ◽  
2002 ◽  
Vol 40 (2) ◽  
pp. 63-70 ◽  
Author(s):  
Hiro Ito ◽  
Motoyasu Ito ◽  
Yuichiro Itatsu ◽  
Kazuhiro Nakai ◽  
Hideyuki Uehara ◽  
...  
Keyword(s):  
Source Location ◽  
Location Problems ◽  
Vertex Connectivity ◽  
Edge Connectivity

scholarly journals The Multi-Commodity Source Location Problems and the Price of Greed

2009 ◽  
Vol 13 (1) ◽  
pp. 55-73
Author(s):  
Hiro Ito ◽  
Mike Paterson ◽  
Kenya Sugihara
Keyword(s):  
Source Location ◽  
Location Problems

scholarly journals Connectivity in Hypergraphs

2018 ◽  
Vol 61 (2) ◽  
pp. 252-271 ◽  
Author(s):  
Megan Dewar ◽  
David Pike ◽  
John Proos
Keyword(s):  
Polynomial Time ◽  
The Other ◽  
Np Hard ◽  
Vertex Connectivity ◽  
Edge Connectivity ◽  
The Relationship ◽  
Weak Edge ◽  
Edge Size

AbstractIn this paper we consider two natural notions of connectivity for hypergraphs: weak and strong. We prove that the strong vertex connectivity of a connected hypergraph is bounded by its weak edge connectivity, thereby extending a theorem of Whitney from graphs to hypergraphs. We find that, while determining a minimum weak vertex cut can be done in polynomial time and is equivalent to finding a minimum vertex cut in the 2-section of the hypergraph in question, determining a minimum strong vertex cut is NP-hard for general hypergraphs. Moreover, the problem of finding minimum strong vertex cuts remains NP-hard when restricted to hypergraphs with maximum edge size at most 3. We also discuss the relationship between strong vertex connectivity and the minimum transversal problem for hypergraphs, showing that there are classes of hypergraphs for which one of the problems is NP-hard, while the other can be solved in polynomial time.

scholarly journals The source location problem with local 3-vertex-connectivity requirements

2007 ◽  
Vol 155 (18) ◽  
pp. 2523-2538 ◽  
Author(s):  
Toshimasa Ishii ◽  
Hitoshi Fujita ◽  
Hiroshi Nagamochi
Keyword(s):  
Location Problem ◽  
Source Location ◽  
Vertex Connectivity
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