scholarly journals Destroying Noncomplete Regular Components in Graph Partitions

2012 ◽  
Vol 72 (2) ◽  
pp. 123-127 ◽  
Author(s):  
Landon Rabern
Keyword(s):  
Graph Partitions

Spanning Properties of Yao and 𝜃-Graphs in the Presence of Constraints

2019 ◽  
Vol 29 (02) ◽  
pp. 95-120 ◽  
Author(s):  
Prosenjit Bose ◽  
André van Renssen
Keyword(s):  
Line Segment ◽  
Large Family ◽  
Upper Bounds ◽  
The Other ◽  
Additional Property ◽  
Graph Partitions ◽  
Set Of Points ◽  
The Given

We present improved upper bounds on the spanning ratio of constrained [Formula: see text]-graphs with at least 6 cones and constrained Yao-graphs with 5 or at least 7 cones. Given a set of points in the plane, a Yao-graph partitions the plane around each vertex into [Formula: see text] disjoint cones, each having aperture [Formula: see text], and adds an edge to the closest vertex in each cone. Constrained Yao-graphs have the additional property that no edge properly intersects any of the given line segment constraints. Constrained [Formula: see text]-graphs are similar to constrained Yao-graphs, but use a different method to determine the closest vertex. We present tight bounds on the spanning ratio of a large family of constrained [Formula: see text]-graphs. We show that constrained [Formula: see text]-graphs with [Formula: see text] ([Formula: see text] and integer) cones have a tight spanning ratio of [Formula: see text], where [Formula: see text] is [Formula: see text]. We also present improved upper bounds on the spanning ratio of the other families of constrained [Formula: see text]-graphs. These bounds match the current upper bounds in the unconstrained setting. We also show that constrained Yao-graphs with an even number of cones ([Formula: see text]) have spanning ratio at most [Formula: see text] and constrained Yao-graphs with an odd number of cones ([Formula: see text]) have spanning ratio at most [Formula: see text]. As is the case with constrained [Formula: see text]-graphs, these bounds match the current upper bounds in the unconstrained setting, which implies that like in the unconstrained setting using more cones can make the spanning ratio worse.

The Price of Order

2016 ◽  
Vol 26 (03n04) ◽  
pp. 135-149
Author(s):  
Prosenjit Bose ◽  
Pat Morin ◽  
André van Renssen
Keyword(s):  
Lower Bounds ◽  
Large Family ◽  
Worst Case ◽  
Graph Partitions ◽  
First Results

We present tight bounds on the spanning ratio of a large family of ordered [Formula: see text]-graphs. A [Formula: see text]-graph partitions the plane around each vertex into [Formula: see text] disjoint cones, each having aperture [Formula: see text]. An ordered [Formula: see text]-graph is constructed by inserting the vertices one by one and connecting each vertex to the closest previously-inserted vertex in each cone. We show that for any integer [Formula: see text], ordered [Formula: see text]-graphs with [Formula: see text] cones have a tight spanning ratio of [Formula: see text]. We also show that for any integer [Formula: see text], ordered [Formula: see text]-graphs with [Formula: see text] cones have a tight spanning ratio of [Formula: see text]. We provide lower bounds for ordered [Formula: see text]-graphs with [Formula: see text] and [Formula: see text] cones. For ordered [Formula: see text]-graphs with [Formula: see text] and [Formula: see text] cones these lower bounds are strictly greater than the worst case spanning ratios of their unordered counterparts. These are the first results showing that ordered [Formula: see text]-graphs have worse spanning ratios than unordered [Formula: see text]-graphs. Finally, we show that, unlike their unordered counterparts, the ordered [Formula: see text]-graphs with 4, 5, and 6 cones are not spanners.

scholarly journals Optimising Graph Partitions Using Parallel Evolution

2004 ◽  
pp. 91-102
Author(s):  
R. Baños ◽  
C. Gil ◽  
J. Ortega ◽  
F. G. Montoya
Keyword(s):  
Parallel Evolution ◽  
Graph Partitions

scholarly journals Local Graph Partitions for Approximation and Testing

2009 ◽  
Author(s):  
Avinatan Hassidim ◽  
Jonathan A. Kelner ◽  
Huy N. Nguyen ◽  
Krzysztof Onak
Keyword(s):  
Graph Partitions ◽  
Local Graph

CuSP

2021 ◽  
Vol 55 (1) ◽  
pp. 47-60
Author(s):  
Loc Hoang ◽  
Roshan Dathathri ◽  
Gurbinder Gill ◽  
Keshav Pingali
Keyword(s):  
Single Machine ◽  
Distributed Memory ◽  
The State ◽  
Main Memory ◽  
Input Graph ◽  
Large Graphs ◽  
Graph Analytics ◽  
Graph Partitions ◽  
High Level ◽  
Edge Partitioning

Graph analytics systems must analyze graphs with billions of vertices and edges which require several terabytes of storage. Distributed-memory clusters are often used for analyzing such large graphs since the main memory of a single machine is usually restricted to a few hundreds of gigabytes. This requires partitioning the graph among the machines in the cluster. Existing graph analytics systems use a built-in partitioner that incorporates a particular partitioning policy, but the best policy is dependent on the algorithm, input graph, and platform. Therefore, built-in partitioners are not sufficiently flexible. Stand-alone graph partitioners are available, but they too implement only a few policies. CuSP is a fast streaming edge partitioning framework which permits users to specify the desired partitioning policy at a high level of abstraction and quickly generates highquality graph partitions. For example, it can partition wdc12, the largest publicly available web-crawl graph with 4 billion vertices and 129 billion edges, in under 2 minutes for clusters with 128 machines. Our experiments show that it can produce quality partitions 6× faster on average than the state-of-theart stand-alone partitioner in the literature while supporting a wider range of partitioning policies.

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