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In the second stage, the target edge set is revealed, and the decision maker can augment the initial vertex subset with additional vertices to ensure coverage; however, this augmentation is more expensive due to increased vertex costs. This paper initiates the study of the two-stage stochastic vertex cover problem in the realm of\n                    <jats:italic>distributed graph algorithms<\/jats:italic>\n                    , where the decision-making process is distributed among the graph\u2019s vertices. We consider two known stochastic optimization variants: the\n                    <jats:italic>independent sampling<\/jats:italic>\n                    model, where the edges in the target set are drawn independently from some probability distribution; and the\n                    <jats:italic>finite scenario<\/jats:italic>\n                    model, where the probability distribution over the target edge set is provided explicitly. For both variants, we devise efficient distributed algorithms based on a novel adaptation of the distributed primal-dual technique to linear programs resulting from the stochastic optimization problems\u2019 relaxation.\n                  <\/jats:p>","DOI":"10.1007\/s00446-025-00486-8","type":"journal-article","created":{"date-parts":[[2025,5,31]],"date-time":"2025-05-31T04:05:53Z","timestamp":1748664353000},"page":"377-395","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Towards distributed two-stage stochastic optimization"],"prefix":"10.1007","volume":"38","author":[{"given":"Yuval","family":"Emek","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Noga","family":"Harlev","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Taisuke","family":"Izumi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,5,31]]},"reference":[{"key":"486_CR1","doi-asserted-by":"crossref","unstructured":"\u00c5strand, M., Suomela, J.: (2010) Fast distributed approximation algorithms for vertex cover and set cover in anonymous networks. 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