A GRAPH BASED DAVIDSON ALGORITHM FOR THE GRAPH PARTITIONING PROBLEM

1999 ◽  
Vol 10 (02) ◽  
pp. 225-246 ◽  
Author(s):  
MICHAEL HOLZRICHTER ◽  
SUELY OLIVEIRA
Keyword(s):  
Graph Theory ◽  
Load Balancing ◽  
Graph Partitioning ◽  
Graph Laplacian ◽  
Matrix Factorizations ◽  
Graph Partitioning Problem ◽  
Spectral Graph ◽  
Partitioning Problem ◽  
Davidson Algorithm ◽  
Spectral Graph Partitioning

The problem of partitioning a graph such that the number of edges incident to vertices in different partitions is minimized, arises in many contexts. Some examples include its recursive application for minimizing fill-in in matrix factorizations and load-balancing for parallel algorithms. Spectral graph partitioning algorithms partition a graph using the eigenvector associated with the second smallest eigenvalue of a matrix called the graph Laplacian. The focus of this paper is the use graph theory to compute this eigenvector more quickly.

scholarly journals K-way Balanced Graph Partitioning for Parallel Computing

2021 ◽  
Vol 22 (4) ◽  
pp. 413-424
Author(s):  
Siddheshwar Vilas Patil ◽  
Dinesh B. Kulkarni
Keyword(s):  
Parallel Computing ◽  
Load Balancing ◽  
Graph Partitioning ◽  
High Performance ◽  
Ground Truth ◽  
Complex Problem ◽  
Maximum Throughput ◽  
Graph Partitioning Problem ◽  
Use Of Resources ◽  
Partitioning Problem

In modern computing, high-performance computing (HPC) and parallel computing require most of the decision-making in terms of distributing the payloads (input) uniformly across the available set of resources, majorly processors; the former deals with the hardware and its better utilization. In parallel computing, a larger, complex problem is broken down into multiple smaller calculations and executed simultaneously on several processors. The efficient use of resources (processors) plays a vital role in achieving the maximum throughput which necessitates uniform load distribution across available processors, i.e. load balancing. The load balancing in parallel computing is modeled as a graph partitioning problem. In the graph partitioning problem, the weighted nodes represent the computing cost at each node, and the weighted edges represent the communication cost between the connected nodes. The goal is to partition the graph G into k partitions such that: I) the sum of weights on the nodes is approximately equal for each partition, and, II) the sum of weights on the edges across different partitions is minimum.  In this paper, a novel node-weighted and edge-weighted k-way balanced graph partitioning (NWEWBGP) algorithm of  O(n x n)  is proposed. The algorithm works for all relevant values of k, meets or improves on earlier algorithms in terms of balanced partitioning and lowest edge-cut. For evaluation and validation, the outcome is compared with the ground truth benchmarks.

scholarly journals Image Segmentation using Euler Graphs

2010 ◽  
Vol 5 (3) ◽  
pp. 314 ◽  
Author(s):  
T.N. Janakiraman ◽  
P.V.S.S.R. Chandra Mouli
Keyword(s):  
Image Segmentation ◽  
Graph Theory ◽  
Polynomial Time ◽  
Graph Partitioning ◽  
Finite Graph ◽  
Objective Evaluation ◽  
Graph Partitioning Problem ◽  
Partitioning Problem ◽  
As Graph ◽  
Segmentation Problem

This paper presents a new algorithm for image segmentation problem using the concepts of Euler graphs in graph theory. By treating image as an undirected weighted non-planar finite graph (G), image segmentation is handled as graph partitioning problem. The proposed method locates region boundaries or clusters and runs in polynomial time. Subjective comparison and objective evaluation shows the efficacy of the proposed approach in different image domains.

FINAL VERSION.pdf

2019 ◽  
Author(s):  
Nasir Saeed ◽  
Mohamed-Slim Alouini ◽  
Tareq Y. Al-Naffouri
Keyword(s):  
Graph Partitioning ◽  
Three Dimensional ◽  
Smart Objects ◽  
Localization Technique ◽  
Optical Internet ◽  
Spectral Graph ◽  
Accurate Localization ◽  
Spectral Graph Partitioning ◽  
Link Connectivity

<div>Localization is a fundamental task for optical internet</div><div>of underwater things (O-IoUT) to enable various applications</div><div>such as data tagging, routing, navigation, and maintaining link connectivity. The accuracy of the localization techniques for OIoUT greatly relies on the location of the anchors. Therefore, recently localization techniques for O-IoUT which optimize the anchor’s location are proposed. However, optimization of anchors location for all the smart objects in the network is not a useful solution. Indeed, in a network of densely populated smart objects, the data collected by some sensors are more valuable than the data collected from other sensors. Therefore, in this paper, we propose a three-dimensional accurate localization technique by optimizing the anchor’s location for a set of smart objects. Spectral graph partitioning is used to select the set of valuable</div><div>sensors.</div>

Efficient nuclei segmentation based on spectral graph partitioning

2016 ◽  
Author(s):  
Gwo Giun Chris Lee ◽  
Shi-Yu Hung ◽  
Tai-Ping Wang ◽  
Chun-Fu Richard Chen ◽  
Chi-Kuang Sun ◽  
...  
Keyword(s):  
Graph Partitioning ◽  
Nuclei Segmentation ◽  
Spectral Graph ◽  
Spectral Graph Partitioning
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