The node capacitated graph partitioning problem: A computational study (original) (raw)
Related papers
2022
In this work, a graph partitioning problem in a fixed number of connected components is considered. Given an undirected graph with costs on the edges, the problem consists on partitioning the set of nodes into a fixed number of subsets with minimum size, where each subset induces a connected subgraph with minimal edge cost. Mixed Integer Programming formulations together with a variety of valid inequalities are demonstrated and implemented in a Branch & Cut framework. A column generation approach is also proposed for this problem with additional cuts. Finally, the methods are tested for several simulated instances and computational results are discussed.
A Parallel Implementation for Graph Partitioning Heuristics
International Conference on Advances in Computing and Information Technology - ACIT 2014, 2014
The Graph Partitioning Problem (GPP) has several practical applications in many areas, such as design of VLSI (Very-large-scale integration) circuits, solution of numerical methods for simulation problems that include factorization of sparse matrix and partitioning of finite elements meshes for parallel programming applications, between others. The GPP tends to be NP-hard and optimal solutions for solving them are infeasible when the number of vertices of the graph is very large. There has been an increased used of heuristic and metaheuristic algorithms to solve the PPG to get good results where exceptional results are not obtainable by practical means. This article proposes an efficient parallel solution to the GPP problem based on the implementation of existing heuristics in a computational cluster. The proposed solution improves the execution time and, by introducing some random features into the original heuristics, improve the quality of the created partitions.
Iterative partitioning with varying node weights
2000
The balanced partitioning problem divides the nodes of a [hyper] graph into groups of approximately equal weight (ie, satisfying balance constraints) while minimizing the number of [hyper] edges that are cut (ie, adjacent to nodes in different groups). Classic iterative algorithms use the pass paradigm [24] in performing single-node moves [16, 13] to improve the initial solution. To satisfy particular balance constraints, it is usual to require that intermediate solutions satisfy the constraints. Hence, many possible moves are rejected.
An efficient practical heuristic for good ratio-cut partitioning
16th International Conference on VLSI Design, 2003. Proceedings.
We present an efficient heuristic for finding good bipartitions of the vertex set of a graph in the sense of the wellknown measure of ratioCut [2, 8] (essentially the ratio between weight of cut edges and the product of weights of the nodesets of the bipartition). The widely accepted ratioCut bipartitioning algorithm of Wei and Cheng [13] is similar in spirit to the Fiduccia-Mattheyeses [9] algorithm (F-M algorithm). Our approach makes use of F-M algorithm as the first phase that takes in as an input, random bipartitions. In the later phase of our algorithm we make use of a new coarsening strategy and follow it up with a submodular function optimization algorithm on the coarsened graph. We also present the comparison of results of this approach applied to benchmark circuits with the well-established algorithms such as the Wei-Cheng algorithm [13] for ratioCut bipartitioning and pmetis of Metis [7] package. The comparative study not only shows that this new approach indeed produces good quality ratioCut bipartitions, but also the fact that this approach has the potential of finding a large number of such good partitions in comparison with other approaches. The key subroutine in our heuristic strategies is based on the recent finding published in [12] about the role of submodular functions in designing new heuristics and approximate algorithms to some NP-hard problems.
An Improved Node Partitioning Algorithm for the CMST Problem
The capacitated minimum spanning tree (CMST) problem is one of the most fundamental and significant problems in the optimal design of communication networks. In this paper several methods are proposed to improve existing node-oriented branch and bound algorithm for the CMST problem. Techniques for acquiring tighter lower bound are emphasized, while regulations for faster traversing of the search tree are proposed on the basis of comprehensive observation of the search procedure. Computational experiences demonstrate that the proposed methods significantly improved the efficiency of the existing algorithms. Moreover, as an exact algorithm, the proposed one is the first algorithm that solved the 41 node te-class benchmark problem instances.
Application of Parallel and Hybrid Metaheuristics for Graph Partitioning Problem
Numerical Methods and Applications, 2019
In this paper parallel and hybrid metaheuristics for graph partitioning are compared taking into account their efficiency in terms of a cost function and computation time. Seventeen methods developed on the basis of evolutionary algorithm, simulated annealing and tabu search are implemented and tested against graph instances computed on the basis of queen graphs from DIMACS repository and a class of random R-MAT graphs. These graphs are supposed to model a class of digital circuits being subject of decomposition into a given number of modules. In partitioning process several additional constraints have to be satisfied in order to enable composition of original circuits from subcircuits by means of VLSI/FPGA modules.
A computational study of graph partitioning
Mathematical Programming, 1994
Let G = (N; E) be an edge-weighted undirected graph. The graph partitioning problem is the problem of partitioning the node set N into k disjoint subsets of speci ed sizes so as to minimize the total weight of the edges connecting nodes in distinct subsets of the partition. We present a numerical study on the use of eigenvalue-based techniques to nd upper and lower bounds for this problem. Results for bisecting graphs with up to several thousand nodes are given, and for small graphs some trisection results are presented. We show that the techniques are very robust and consistently produce upper and lower bounds having a relative gap of typically a few percentage points.
Multilevel algorithms for multi-constraint graph partitioning
1998
Traditional graph partitioning algorithms compute a k-way partitioning of a graph such that the number of edges that are cut by the partitioning is minimized and each partition has an equal number of vertices. The task of minimizing the edge-cut can be considered as the objective and the requirement that the partitions will be of the same size can be considered as the constraint. In this paper we extend the partitioning problem by incorporating an arbitrary number of balancing constraints. In our formulation, a vector of weights is assigned to each vertex, and the goal is to produce a k-way partitioning such that the partitioning satisfies a balancing constraint associated with each weight, while attempting to minimize the edge-cut. Applications of this multi-constraint graph partitioning problem include parallel solution of multi-physics and multi-phase computations, that underly many existing and emerging large-scale scientific simulations. We present new multi-constraint graph partitioning algorithms that are based on the multilevel graph partitioning paradigm. Our work focuses on developing new types of heuristics for coarsening, initial partitioning, and refinement that are capable of successfully handling multiple constraints. We experimentally evaluate the effectiveness of our multi-constraint partitioners on a a variety of synthetically generated problems.