A strong formulation for the graph partition problem

Networks ◽  
2019 ◽  
Vol 75 (2) ◽  
pp. 183-202
Author(s):  
Sunil Chopra ◽  
Sangho Shim
Keyword(s):  
Graph Partition ◽  
Partition Problem ◽  
Strong Formulation

scholarly journals A new multi-level algorithm for balanced partition problem on large scale directed graphs

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Xianyue Li ◽  
Yufei Pang ◽  
Chenxia Zhao ◽  
Yang Liu ◽  
Qingzhen Dong
Keyword(s):  
Large Scale ◽  
Directed Graphs ◽  
Vlsi Design ◽  
Graph Partition ◽  
Partition Problem ◽  
Multi Level ◽  
The Stability ◽  
Recursive Partition ◽  
Balanced Partition ◽  
Partition Method

AbstractGraph partition is a classical combinatorial optimization and graph theory problem, and it has a lot of applications, such as scientific computing, VLSI design and clustering etc. In this paper, we study the partition problem on large scale directed graphs under a new objective function, a new instance of graph partition problem. We firstly propose the modeling of this problem, then design an algorithm based on multi-level strategy and recursive partition method, and finally do a lot of simulation experiments. The experimental results verify the stability of our algorithm and show that our algorithm has the same good performance as METIS. In addition, our algorithm is better than METIS on unbalanced ratio.

scholarly journals A P-complete graph partition problem

1990 ◽  
Vol 76 (2-3) ◽  
pp. 343-351
Author(s):  
R. Sarnath ◽  
Xin He
Keyword(s):  
Complete Graph ◽  
Graph Partition ◽  
Partition Problem

The bottleneck graph partition problem

Networks ◽  
1996 ◽  
Vol 28 (4) ◽  
pp. 221-225 ◽  
Author(s):  
Dorit S. Hochbaum ◽  
Anu Pathria
Keyword(s):  
Graph Partition ◽  
Partition Problem

A Graph Partition Problem

2015 ◽  
Vol 122 (10) ◽  
pp. 972
Author(s):  
Sebastian M. Cioabă ◽  
Peter J. Cameron
Keyword(s):  
Graph Partition ◽  
Partition Problem

A note on the bottleneck graph partition problem

Networks ◽  
1999 ◽  
Vol 33 (3) ◽  
pp. 189-191 ◽  
Author(s):  
Bettina Klinz ◽  
Gerhard J. Woeginger
Keyword(s):  
Graph Partition ◽  
Partition Problem

EFFICIENT APPROXIMATION ALGORITHMS FOR PAIRWISE DATA CLUSTERING AND APPLICATIONS

2004 ◽  
Vol 14 (01n02) ◽  
pp. 85-104 ◽  
Author(s):  
XIAODONG WU ◽  
DANNY Z. CHEN ◽  
JAMES J. MASON ◽  
STEVEN R. SCHMID
Keyword(s):  
Polynomial Time ◽  
Data Clustering ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Approximation Ratio ◽  
Graph Partition ◽  
Partition Problem ◽  
Normalized Cut ◽  
Clustering Problem ◽  
Approximation Polynomial

Data clustering is an important theoretical topic and a sharp tool for various applications. It is a task frequently arising in geometric computing. The main objective of data clustering is to partition a given data set into clusters such that the data items within the same cluster are "more" similar to each other with respect to certain measures. In this paper, we study the pairwise data clustering problem with pairwise similarity/dissimilarity measures that need not satisfy the triangle inequality. By using a criterion, called the minimum normalized cut, we model the general pairwise data clustering problem as a graph partition problem. The graph partition problem based on minimizing the normalized cut is known to be NP-hard. For an undirected weighted graph of n vertices, we present a ((4+o(1)) In n)-approximation polynomial time algorithm for the minimum normalized cut problem; this is the first provably good approximation polynomial time algorithm for the problem. We also give a more efficient algorithm for this problem by sacrificing the approximation ratio slightly. Further, our scheme achieves a ((2+o(1)) In n)-approximation polynomial time algorithm for computing the sparsest cuts in edge-weighted and vertex-weighted undirected graphs, improving the previously best known approximation ratio by a constant factor. Some applications and implementation work of our approximation normalized cut algorithms are also discussed.

A graph partition problem

1996 ◽  
Vol 12 (4) ◽  
pp. 393-400 ◽  
Author(s):  
Yanpei Liu ◽  
Morgana Aurora ◽  
Simeone Bruno
Keyword(s):  
Graph Partition ◽  
Partition Problem

On a graph partition problem with application to VLSI layout

1992 ◽  
Vol 43 (2) ◽  
pp. 87-94 ◽  
Author(s):  
Arunabha Sen ◽  
Haiyong Deng ◽  
Sumanta Guha
Keyword(s):  
Graph Partition ◽  
Partition Problem ◽  
Vlsi Layout

scholarly journals A New Multi-level Algorithms for Balanced Partition Problem on Large Scale Directed Graphs

2021 ◽  
Author(s):  
Xianyue Li ◽  
Yufei Pang ◽  
Chenxia Zhao ◽  
Yang Liu ◽  
Qingzhen Dong
Keyword(s):  
Large Scale ◽  
Directed Graphs ◽  
Vlsi Design ◽  
Graph Partition ◽  
Partition Problem ◽  
Multi Level ◽  
The Stability ◽  
Recursive Partition ◽  
Balanced Partition ◽  
Partition Method

Abstract Graph partition is a classical combinatorial optimization and graph theory problem, and it has a lot of applications, such as scientific computing, VLSI design and clustering etc. In this paper, we study the partition problem on large scale directed graphs under a new objective function, a new case of graph partition problem. We firstly propose the modeling of this problem, then design an algorithm based on multi-level strategy and recursive partition method, and finally do a lot of simulation experiments. The experimental results verify the stability of our algorithm and show that our algorithm has the same good performance as METIS. In addition, our algorithm is better than METIS on unbalanced ratio.

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