A separator theorem for graphs of bounded genus
Journal of Algorithms
An iterative method for elliptic problems on regions partitioned into substructures
Mathematics of Computation
Parallel computation with adaptive methods for elliptic and hyperbolic systems
Computer Methods in Applied Mechanics and Engineering
A separator theorem for graphs with an excluded minor and its applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Separators for sphere-packings and nearest neighbor graphs
Journal of the ACM (JACM)
How Good is Recursive Bisection?
SIAM Journal on Scientific Computing
Provably Good Partitioning and Load Balancing Algorithms for Parallel Adaptive N-Body Simulation
SIAM Journal on Scientific Computing
Geometric Mesh Partitioning: Implementation and Experiments
SIAM Journal on Scientific Computing
Spectral partitioning works: planar graphs and finite element meshes
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
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Domain decomposition is one of the most effective and popular parallel computing techniques for solving large scale numerical systems. In the special case when the amount of computation in a subdomain is proportional to the volume of the subdomain, domain decomposition amounts to minimizing the surface area of each subdomain while dividing the volume evenly. Motivated by this fact, we study the following min-max boundary multi-way partitioning problem: Given a graph G and an integer k 1, we would like to divide G into k subgraphs G1,..., Gk (by removing edges) such that (i) |Gi| = Θ(|G|/k) for all i ∈ {1,..., k}; and (ii) the maximum boundary size of any subgraph (the set of edges connecting it with other subgraphs) is minimized. We provide an algorithm that given G, a well-shaped mesh in d dimensions, finds a partition of G into k subgraphs G1, ..., Gk, such that for all i, Gi has Θ(|G|/k) vertices and the number of edges connecting Gi with the other subgraphs is O((|G|/k)1-1/d). Our algorithm can find such a partition in O(|G| log k) time. Finally, we extend our results to vertex-weighted and vertex-based graph decomposition. Our results can be used to simultaneously balance the computational and memory requirement on a distributed-memory parallel computer without sacrificing the communication overhead.