Finding near-optimal independent sets at scale

Lamm, Sebastian; Sanders, Peter; Schulz, Christian; Strash, Darren; Werneck, Renato F.

doi:10.1007/s10732-017-9337-x

Cited by 45 publications

(63 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Given that a lot of graph libraries provide independent set algorithms it is also very easy to apply by taking an existing implementation. The algorithm KAMIS [19] computes large independent sets by a combination of several advanced algorithmic techniques such as graph partitioning and kernelization. Finally we designed a new exact algorithm (MHS) based on a MAXSAT formulation.…”

Section: Labeling Algorithmsmentioning

confidence: 99%

See 1 more Smart Citation

Exploring Semi-Automatic Map Labeling

Klute

Löffler

et al. 2019

Proceedings of the 27th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems

View full text Add to dashboard Cite

Label placement in maps is a very challenging task that is critical for the overall map quality. Most previous work focused on designing and implementing fully automatic solutions, but the resulting visual and aesthetic quality has not reached the same level of sophistication that skilled human cartographers achieve. We investigate a different strategy that combines the strengths of humans and algorithms. In our proposed method, first an initial labeling is computed that has many well-placed labels but is not claiming to be perfect. Instead it serves as a starting point for an expert user who can then interactively and locally modify the labeling where necessary. In an iterative human-in-the-loop process alternating between user modifications and local algorithmic updates and refinements the labeling can be tuned to the user's needs.We demonstrate our approach by performing different possible modification steps in a sample workflow with a prototypical interactive labeling editor. Further, we report computational performance results from a simulation experiment in QGIS, which investigates the differences between exact and heuristic algorithms for semi-automatic map labeling. To that end, we compare several alternatives for recomputing the labeling after local modifications and updates, as a major ingredient for an interactive labeling editor.

show abstract

Section: Labeling Algorithmsmentioning

confidence: 99%

“…KAMIS The third algorithm KAMIS is based on the maximum independent set solver framework KaMIS [19]. By combining kernelization, local search, an evolutionary algorithm, graph partitioning and other techniques, this advanced maximum independent solver can very successfully find large independent sets in huge sparse graphs.…”

Section: Labeling Algorithmsmentioning

confidence: 99%

Exploring Semi-Automatic Map Labeling

Klute

Löffler

et al. 2019

Proceedings of the 27th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems

View full text Add to dashboard Cite

show abstract

“…Kernelization and reductions play an important role in heuristic algorithms too. Lamm et al [31] showed that including reductions in a branch-and-reduce inspired evolutionary algorithm enables finding exact solutions much faster than provably exact algorithms. Dahlum et al [15] further showed how to effectively combine reductions with local search.…”

Section: Heuristicmentioning

confidence: 99%

“…However, kernelization may also be applied repeatedly as part of an algorithm [2,12,31]. In either case, the smallest kernels (or seemingly equivalently, the most varied reductions) give the best chance at finding solutions.…”

Section: Introductionmentioning

confidence: 99%

“…In either case, the smallest kernels (or seemingly equivalently, the most varied reductions) give the best chance at finding solutions. For instance, the reductions used by Akiba and Iwata [2] are the only ones known to compute an exact MIS on certain large-scale graphs, and these reductions are further successful in computing exact solutions in an evolutionary approach [31]. However it is not always beneficial to compute the smallest kernel possible.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Scalable Kernelization for Maximum Independent Sets

Hespe¹,

Schulz²,

Strash³

2018

2018 Proceedings of the Twentieth Workshop on Algorithm Engineering and Experiments (ALENEX)

Self Cite

View full text Add to dashboard Cite

The most efficient algorithms for finding maximum independent sets in both theory and practice use reduction rules to obtain a much smaller problem instance called a kernel. The kernel can then be solved quickly using exact or heuristic algorithms-or by repeatedly kernelizing recursively in the branch-and-reduce paradigm. It is of critical importance for these algorithms that kernelization is fast and returns a small kernel. Current algorithms are either slow but produce a small kernel, or fast and give a large kernel. We attempt to accomplish both of these goals simultaneously, by giving an efficient parallel kernelization algorithm based on graph partitioning and parallel bipartite maximum matching.We combine our parallelization techniques with two techniques to accelerate kernelization further: dependency checking that prunes reductions that cannot be applied, and reduction tracking that allows us to stop kernelization when reductions become less fruitful. Our algorithm produces kernels that are orders of magnitude smaller than the fastest kernelization methods, while having a similar execution time. Furthermore, our algorithm is able to compute kernels with size comparable to the smallest known kernels, but up to two orders of magnitude faster than previously possible. Finally, we show that our kernelization algorithm can be used to accelerate existing state-of-the-art heuristic algorithms, allowing us to find larger independent sets faster on large real-world networks and synthetic instances.

show abstract

Simple iterative trial search for the maximum independent set problem optimized for the GPUs

Imanaga

Nakano

Yasudo

et al. 2021

Concurrency and Computation

View full text Add to dashboard Cite

An independent set of a graph is a subset of the nodes such that no two nodes in it are adjacent. The maximum independent set (MIS) problem is an optimization problem to find a largest independent set. The main contribution of this article is to introduce a generic iterative trial search algorithm that we call iMIS for finding approximate solutions for the MIS problem. The generic algorithm iMIS is designed so that it can be implemented to run on GPUs very efficiently. Since the performance of the algorithm varies depending on its search strategy, we present a hybrid algorithm that combines three strategies of the iMIS such that best one of them for an input graph is automatically selected. We have implemented our hybrid algorithm to run on a multi‐GPU server with eight NVIDIA A100 GPUs. And evaluated the performance for 66 DIMACS benchmark graphs and 78 random graphs with up to 256M nodes. We have also evaluated the performance of three previously published algorithms for the MIS problem and an approach using Gurobi linear programming solver. The experimental results show that our hybrid algorithm can find larger independent sets for all 144 graphs compared to other methods.

show abstract

Finding near-optimal independent sets at scale

Cited by 45 publications

References 53 publications

Exploring Semi-Automatic Map Labeling

Exploring Semi-Automatic Map Labeling

Scalable Kernelization for Maximum Independent Sets

Simple iterative trial search for the maximum independent set problem optimized for the GPUs

Contact Info

Product

Resources

About