{"abstract":[{"text":"The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. Here, we introduce a linear-time algorithm to compute near-minimum cuts. Our algorithm is based on cluster contraction using label propagation and Padberg and Rinaldi's contraction heuristics [SIAM Review, 1991]. We give both sequential and shared-memory parallel implementations of our algorithm. Extensive experiments on both real-world and generated instances show that our algorithm finds the optimal cut on nearly all instances significantly faster than other state-of-the-art exact algorithms, and our error rate is lower than that of other heuristic algorithms. In addition, our parallel algorithm shows good scalability.","lang":"eng"}],"status":"public","_id":"11882","page":"48-61","main_file_link":[{"url":"https://arxiv.org/abs/1708.06127","open_access":"1"}],"day":"01","publisher":"Society for Industrial and Applied Mathematics","author":[{"orcid":"0000-0002-5008-6530","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","full_name":"Henzinger, Monika H","last_name":"Henzinger","first_name":"Monika H"},{"full_name":"Noe, Alexander","last_name":"Noe","first_name":"Alexander"},{"first_name":"Christian","last_name":"Schulz","full_name":"Schulz, Christian"},{"last_name":"Strash","full_name":"Strash, Darren","first_name":"Darren"}],"publication":"20th Workshop on Algorithm Engineering and Experiments","type":"conference","extern":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2023-02-17T14:03:39Z","conference":{"name":"ALENEX: Symposium on Algorithm Engineering and Experiments","start_date":"2018-01-07","location":"New Orleans, LA, United States","end_date":"2018-01-08"},"date_created":"2022-08-17T07:04:57Z","publication_identifier":{"eisbn":["978-1-61197-505-5"]},"year":"2018","oa":1,"title":"Practical minimum cut algorithms","language":[{"iso":"eng"}],"scopus_import":"1","quality_controlled":"1","oa_version":"Preprint","external_id":{"arxiv":["1708.06127"]},"date_published":"2018-01-01T00:00:00Z","publication_status":"published","month":"01","citation":{"apa":"Henzinger, M. H., Noe, A., Schulz, C., &#38; Strash, D. (2018). Practical minimum cut algorithms. In <i>20th Workshop on Algorithm Engineering and Experiments</i> (pp. 48–61). New Orleans, LA, United States: Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/1.9781611975055.5\">https://doi.org/10.1137/1.9781611975055.5</a>","mla":"Henzinger, Monika H., et al. “Practical Minimum Cut Algorithms.” <i>20th Workshop on Algorithm Engineering and Experiments</i>, Society for Industrial and Applied Mathematics, 2018, pp. 48–61, doi:<a href=\"https://doi.org/10.1137/1.9781611975055.5\">10.1137/1.9781611975055.5</a>.","ista":"Henzinger MH, Noe A, Schulz C, Strash D. 2018. Practical minimum cut algorithms. 20th Workshop on Algorithm Engineering and Experiments. ALENEX: Symposium on Algorithm Engineering and Experiments, 48–61.","short":"M.H. Henzinger, A. Noe, C. Schulz, D. Strash, in:, 20th Workshop on Algorithm Engineering and Experiments, Society for Industrial and Applied Mathematics, 2018, pp. 48–61.","ama":"Henzinger MH, Noe A, Schulz C, Strash D. Practical minimum cut algorithms. In: <i>20th Workshop on Algorithm Engineering and Experiments</i>. Society for Industrial and Applied Mathematics; 2018:48-61. doi:<a href=\"https://doi.org/10.1137/1.9781611975055.5\">10.1137/1.9781611975055.5</a>","ieee":"M. H. Henzinger, A. Noe, C. Schulz, and D. Strash, “Practical minimum cut algorithms,” in <i>20th Workshop on Algorithm Engineering and Experiments</i>, New Orleans, LA, United States, 2018, pp. 48–61.","chicago":"Henzinger, Monika H, Alexander Noe, Christian Schulz, and Darren Strash. “Practical Minimum Cut Algorithms.” In <i>20th Workshop on Algorithm Engineering and Experiments</i>, 48–61. Society for Industrial and Applied Mathematics, 2018. <a href=\"https://doi.org/10.1137/1.9781611975055.5\">https://doi.org/10.1137/1.9781611975055.5</a>."},"article_processing_charge":"No","doi":"10.1137/1.9781611975055.5"}