Partitioning Complex Networks via Size-constrained Clustering

The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and edges until the graph is small enough to be partitioned by some other algorithm. A partition of the input graph is then constructed by successively transferring the solution to the next finer graph and applying a local search algorithm to improve the current solution. In this paper, we describe a novel approach to partition graphs effectively especially if the networks have a highly irregular structure. More precisely, our algorithm provides graph coarsening by iteratively contracting size-constrained clusterings that are computed using a label propagation algorithm. The same algorithm that provides the size-constrained clusterings can also be used during uncoarsening as a fast and simple local search algorithm. Depending on the algorithm's configuration, we are able to compute partitions of very high quality outperforming all competitors, or partitions that are comparable to the best competitor in terms of quality, hMetis, while being nearly an order of magnitude faster on average. The fastest configuration partitions the largest graph available to us with 3.3 billion edges using a single machine in about ten minutes while cutting less than half of the edges than the fastest competitor, kMetis

Optimal clustering of frequency-constrained maintenance jobs with shared set-ups

Since maintenance jobs often require one or more set-up activities, joint execution or clustering of maintenance jobs is a powerful instrument to reduce shut-down costs. We consider a clustering problem for frequency-constrained maintenance jobs, i.e. maintenance jobs that must be carried out with a prescribed (or higher) frequency. For the clustering of maintenance jobs with identical, so-called common set-ups, several strong dominance rules are provided. These dominance rules are used in an efficient dynamic programming algorithm which solves the problem in polynomial time. For the clustering of maintenance jobs with partially identical, so-called shared set-ups, similar but less strong dominance rules are available. Nevertheless, a surprisingly well-performing greedy heuristic and a branch and bound procedure have been developed to solve this problem. For randomly generated test problems with 10 set-ups and 30 maintenance jobs, the heuristic was optimal in 47 out of 100 test problems, with an average deviation of 0.24% from the optimal solution. In addition, the branch and bound method found an optimal solution in only a few seconds computation time on average