Definitions
Given an input graph G = (V, E) and an integer k ≥ 2, the graph partitioning problem is to divide V into k disjoint blocks of vertices V1, V2, …, Vk, such that ∪1≤i≤kVi = V , while simultaneously optimizing an objective function and maintaining balance: \(|V_i|\leq (1+\epsilon )\left \lceil |V| / k\right \rceil \) for some 𝜖 ≥ 0.
Overview
Subdividing a problem into manageable pieces is a critical task in effectively parallelizing computation and even accelerating sequential computation. A key method that has received a lot of attention for doing so is graph partitioning. The simplest and most common form of graph partitioning asks for the vertex set to be partitioned into k roughly equal-sized blocks while minimizing the number of edges between the blocks (called cut edges). Even this most basic variant is NP-hard (Hyafil and Rivest 1973). Graph partitioning has many application areas, including VLSI (Karypis et al. 1999), scientific computing (Langguth et al. 2015),...
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Schulz, C., Strash, D. (2019). Graph Partitioning: Formulations and Applications to Big Data. In: Sakr, S., Zomaya, A.Y. (eds) Encyclopedia of Big Data Technologies. Springer, Cham. https://doi.org/10.1007/978-3-319-77525-8_312
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