Dynamic Balanced Graph Partitioning

This paper initiates the study of the classic balanced graph partitioning problem from an online perspective: Given an arbitrary sequence of pairwise communication requests between $n$ nodes, with patterns that may change over time, the objective is to service these requests efficiently by partitioning the nodes into $\ell$ clusters, each of size $k$, such that frequently communicating nodes are located in the same cluster. The partitioning can be updated dynamically by migrating nodes between clusters. The goal is to devise online algorithms which jointly minimize the amount of inter-cluster communication and migration cost. The problem features interesting connections to other well-known online problems. For example, scenarios with $\ell=2$ generalize online paging, and scenarios with $k=2$ constitute a novel online variant of maximum matching. We present several lower bounds and algorithms for settings both with and without cluster-size augmentation. In particular, we prove that any deterministic online algorithm has a competitive ratio of at least $k$, even with significant augmentation. Our main algorithmic contributions are an $O(k \log{k})$-competitive deterministic algorithm for the general setting with constant augmentation, and a constant competitive algorithm for the maximum matching variant

Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions

An effective multilevel tabu search approach for balanced graph partitioning

Graph partitioning is one of the fundamental NP-complete problems which is widely applied in many domains, such as VLSI design, image segmentation, data mining, etc. Given a graph G=(V,E), the balanced k-partitioning problem consists in partitioning the vertex set V into k disjoint subsets of about the same size, such that the number of cutting edges is minimized. In this paper, we present a multilevel algorithm for balanced partition, which integrates a powerful refinement procedure based on tabu search with periodic perturbations. Experimental evaluations on a wide collection of benchmark graphs show that the proposed approach not only competes very favorably with the two well-known partitioning packages METIS and CHACO, but also improves more than two thirds of the best balanced partitions ever reported in the literature

ILP-based Local Search for Graph Partitioning

Computing high-quality graph partitions is a challenging problem with numerous applications. In this paper, we present a novel meta-heuristic for the balanced graph partitioning problem. Our approach is based on integer linear programs that solve the partitioning problem to optimality. However, since those programs typically do not scale to large inputs, we adapt them to heuristically improve a given partition. We do so by defining a much smaller model that allows us to use symmetry breaking and other techniques that make the approach scalable. For example, in Walshaw\u27s well-known benchmark tables we are able to improve roughly half of all entries when the number of blocks is high

Distance-based exponential probability models on constrained combinatorial optimization problems

Estimation of distribution algorithms have already demonstrated their utility when solving a broad range of combinatorial problems. However, there is still room for methodological improvements when approaching constrained type problems. The great majority of works in the literature implement external repairing or penalty schemes, or use ad-hoc sampling methods in order to avoid unfeasible solutions. In this work, we present a new way to develop EDAs for this type of problems by implementing distance-based exponential probability models defined exclusively on the set of feasible solutions. In order to illustrate this procedure, we take the 2-partition balanced Graph Partitioning Problem as a case of study, and design efficient learning and sampling methods in order to use these distance-based probability models in EDAs