Hypergraph Partitioning

Given a hyperedgeand vertex-weighted hypergraph H = (V, E), a k-way partitioning of V assigns the vertices to k disjoint nonempty partitions. The k-way partitioning problem seeks to minimize a given cost function c(P ) whose arguments are partitionings. A standard cost function is net cut,1 which is the sum of weights of hyperedges that are cut by the partitioning (a hyperedge is cut exactly when not all of its vertices are in one partition). Constraints are typically imposed on the partitioning solution, and make the problem difficult. For example, certain vertices can be fixed in particular partitions (fixed constraints). Or, the total vertex weight in each partition may be limited (balance constraints), which results in an NP-hard formulation [21]. Thus, the cost function c(P ) is minimized over the set of feasible solutions Sf , which is a subset of the set of all possible k-way partitionings. Effective move-based heuristics for k-way hypergraph partitioning have been pioneered in such works as [10], [6], [9], with refinements given by [38]. [43], [26], [40], [18], [4], [12], [25], [34], [19] and many others. A comprehensive survey of partitioning formulations and algorithms, centered on VLSI applications and covering move-based, spectral, flow-based, mathematical programming-based, etc. approaches, is given in [5]. A recent update on balanced partitioning in VLSI physical design is provided by [31].