Constrained Min-Cut Replication for K-Way Hypergraph Partitioning

Abstract

R eplication is a widely-used technique in information retrieval and database systems for providing fault tolerance and reducing parallelization and processing costs. Combinatorial models based on hypergraph partitioning are proposed for various problems arising in information retrieval and database systems. We consider the possibility of using vertex replication to improve the quality of hypergraph partitioning. In this study, we focus on the constrained min-cut replication (CMCR) problem, where we are initially given a maximum replication capacity and a K-way hypergraph partition with an initial imbalance ratio. The objective in the CMCR problem is finding the optimal vertex replication sets for each part of the given partition such that the initial cut size of the partition is minimized, where the initial imbalance is either preserved or reduced under the given replication capacity constraint. In this study, we present a complexity analysis of the CMCR problem and propose a model based on a unique blend of coarsening and integer linear programming (ILP) schemes. This coarsening algorithm is derived from a novel utilization of the Dulmage-Mendelsohn decomposition. Experiments show that the ILP formulation coupled with the Dulmage-Mendelsohn decomposition-based coarsening provides high quality results in practical execution times for reducing the cut size of a given K-way hypergraph partition.

ParBFT: An Optimized Byzantine Consensus Parallelism Scheme

“…With the OOP model in Section 4.1 and IOP model in Section 4.2, the final ParBFT optimisation objective function is (22), constrained by ( 23) and (24).…”

“…The authors proved that this optimisation model achieves between 28% and 98% better performance than legacy partitioning schemes. More related partitioning problems (e.g., [24], [25], [26], [27]) have been approached efficiently with mathematical programming, which inspires our optimisation design combined with ParBFT.…”

“…S k c confirm the valid Φ by repeating operations (Lines:[15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] similar to the prepare phase, and finally generate another multi-signature σ ′ and a commit message: ⟨CMT , sn, d ′ , σ ′ , BM ′ Q , t⟩σ p where d ′ =D(Φ) seeing Line: 53. Upon receipt of the commit message, replicas (p k and b k s) of S k c verify the commit message, similarly to the operations in prepare (see Lines: 35-40).…”