Push-relabel based algorithms for the maximum transversal problem

Abstract

We investigate the push-relabel algorithm for solving the problem of finding a maximum cardinality matching in a bipartite graph in the context of the maximum transversal problem. We describe in detail an optimized yet easyto-implement version of the algorithm and fine-tune its parameters. We also introduce new performance-enhancing techniques. On a wide range of realworld instances, we compare the push-relabel algorithm with state-of-the-art algorithms based on augmenting paths and pseudoflows. We conclude that a carefully tuned push-relabel algorithm is competitive with all known augmenting path-based algorithms, and superior to the pseudoflow-based ones.

A Push-Relabel-Based Maximum Cardinality Bipartite Matching Algorithm on GPUs

“…Hence, we set iterGR to 0 (line 3 of Algorithm 3) which stores the iteration number in which the next global relabeling will be performed. Experiments in the literature show that the performance of the algorithm changes drastically with the strategy to set iterGR [7], [16]. In our preliminary experiments, we also observed this sensitivity with different implementations of GETITERGR (line 7 of Algorithm 3).…”

“…For example, it has been shown that when the active columns are visited with a FIFO order, the push-relabel approach obtains a better performance. The most recent implementation and a comparison with the augmenting-path-based algorithms are given by Kaya et al [7]. The authors showed that PR is slightly better than the augmenting-path-based algorithms.…”

“…A threshold of n was suggested as the standard frequency of global relabels [16]. The performance of the push-relabel approach and its several sequential implementations for the bipartite cardinality matching problem have been well studied and various improvements have been proposed [7], [16], [17]. For example, it has been shown that when the active columns are visited with a FIFO order, the push-relabel approach obtains a better performance.…”

“…In our preliminary experiments, we also observed this sensitivity with different implementations of GETITERGR (line 7 of Algorithm 3). In practice, a global relabeling is performed after every k × (n + m) pushes where the suggested k values are between 1 and 2 [7], [16]. Unlike the sequential pushrelabel algorithms, it is very expensive to count the number of pushes performed during kernel executions.…”

“…Their design and careful sequential implementation have been recently investigated. A rigorous set of experiments showed that the push-relabel approach is very promising and performs as good as the augmenting-path-based approach [7]. The implementation of the third, more recent, approach based on pseudoflow algorithms [8], have been described by Chandran and Hochbaum [9].…”