scholarly journals Orientability Thresholds for Random Hypergraphs

2015 ◽  
Vol 24 (5) ◽  
pp. 774-824 ◽  
Author(s):  
PU GAO ◽  
NICHOLAS WORMALD
Keyword(s):  
Load Balancing ◽  
General Version ◽  
Line Load ◽  
Random Hypergraph ◽  
Random Hypergraphs

Leth>w> 0 be two fixed integers. LetHbe a random hypergraph whose hyperedges are all of cardinalityh. Tow-orienta hyperedge, we assign exactlywof its vertices positive signs with respect to the hyperedge, and the rest negative signs. A (w,k)-orientation ofHconsists of aw-orientation of all hyperedges ofH, such that each vertex receives at mostkpositive signs from its incident hyperedges. Whenkis large enough, we determine the threshold of the existence of a (w,k)-orientation of a random hypergraph. The (w,k)-orientation of hypergraphs is strongly related to a general version of the off-line load balancing problem. The graph case, whenh= 2 andw= 1, was solved recently by Cain, Sanders and Wormald and independently by Fernholz and Ramachandran. This settled a conjecture of Karp and Saks.

On-Line Load Balancing for Related Machines

2000 ◽  
Vol 35 (1) ◽  
pp. 108-121 ◽  
Author(s):  
Piotr Berman ◽  
Moses Charikar ◽  
Marek Karpinski
Keyword(s):  
Load Balancing ◽  
Line Load ◽  
On Line ◽  
Related Machines

scholarly journals The Multiple-Orientability Thresholds for Random Hypergraphs

2015 ◽  
Vol 25 (6) ◽  
pp. 870-908 ◽  
Author(s):  
NIKOLAOS FOUNTOULAKIS ◽  
MEGHA KHOSLA ◽  
KONSTANTINOS PANAGIOTOU
Keyword(s):  
Load Balancing ◽  
Hard Disk ◽  
Maximum Load ◽  
Disk Arrays ◽  
Uniform Hypergraph ◽  
Cuckoo Hashing ◽  
Uniform Hypergraphs ◽  
Random Hypergraphs ◽  
Do So ◽  
Parallel Access

Ak-uniform hypergraphH= (V, E) is called ℓ-orientable if there is an assignment of each edgee∈Eto one of its verticesv∈esuch that no vertex is assigned more than ℓ edges. LetHn,m,kbe a hypergraph, drawn uniformly at random from the set of allk-uniform hypergraphs withnvertices andmedges. In this paper we establish the threshold for the ℓ-orientability ofHn,m,kfor allk⩾ 3 and ℓ ⩾ 2, that is, we determine a critical quantityc*k,ℓsuch that with probability 1 −o(1) the graphHn,cn,khas an ℓ-orientation ifc<c*k,ℓ, but fails to do so ifc>c*k,ℓ.Our result has various applications, including sharp load thresholds for cuckoo hashing, load balancing with guaranteed maximum load, and massive parallel access to hard disk arrays.

scholarly journals Threshold and Hitting Time for High-Order Connectedness in Random Hypergraphs

10.37236/5064 ◽  
2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Oliver Cooley ◽  
Mihyun Kang ◽  
Christoph Koch
Keyword(s):  
High Probability ◽  
Hitting Time ◽  
Uniform Hypergraph ◽  
Uniform Hypergraphs ◽  
Time Result ◽  
Edge Probability ◽  
The Moment ◽  
Definition Of ◽  
Random Hypergraph ◽  
Random Hypergraphs

We consider the following definition of connectedness in $k$-uniform hypergraphs: two $j$-sets (sets of $j$ vertices) are $j$-connected if there is a walk of edges between them such that two consecutive edges intersect in at least $j$ vertices. The hypergraph is $j$-connected if all $j$-sets are pairwise $j$-connected. We determine the threshold at which the random $k$-uniform hypergraph with edge probability $p$ becomes $j$-connected with high probability. We also deduce a hitting time result for the random hypergraph process – the hypergraph becomes $j$-connected at exactly the moment when the last isolated $j$-set disappears. This generalises the classical hitting time result of Bollobás and Thomason for graphs.

On-Line Load Balancing with Task Buffer

2017 ◽  
Vol 36 (5) ◽  
pp. 1207-1234
Author(s):  
Jiayin Wei ◽  
Daoyun Xu ◽  
Yongbin Qin ◽  
Ruizhang Huang
Keyword(s):  
Load Balancing ◽  
Line Load ◽  
On Line
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