@article{KlemzRote2022,
  author    = {Klemz, Boris and Rote, G{\"u}nter},
  title     = {Linear-Time Algorithms for Maximum-Weight Induced Matchings and Minimum Chain Covers in Convex Bipartite Graphs},
  series = {Algorithmica},
  volume    = {84},
  journal   = {Algorithmica},
  number    = {4},
  issn      = {1432-0541},
  doi       = {10.1007/s00453-021-00904-w},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-267876},
  pages     = {1064-1080},
  year      = {2022},
  abstract  = {A bipartite graph G=(U,V,E) is convex if the vertices in V can be linearly ordered such that for each vertex u∈U, the neighbors of u are consecutive in the ordering of V. An induced matching H of G is a matching for which no edge of E connects endpoints of two different edges of H. We show that in a convex bipartite graph with n vertices and m weighted edges, an induced matching of maximum total weight can be computed in O(n+m) time. An unweighted convex bipartite graph has a representation of size O(n) that records for each vertex u∈U the first and last neighbor in the ordering of V. Given such a compact representation, we compute an induced matching of maximum cardinality in O(n) time. In convex bipartite graphs, maximum-cardinality induced matchings are dual to minimum chain covers. A chain cover is a covering of the edge set by chain subgraphs, that is, subgraphs that do not contain induced matchings of more than one edge. Given a compact representation, we compute a representation of a minimum chain cover in O(n) time. If no compact representation is given, the cover can be computed in O(n+m) time. All of our algorithms achieve optimal linear running time for the respective problem and model, and they improve and generalize the previous results in several ways: The best algorithms for the unweighted problem versions had a running time of O(n\(^{2}\)) (Brandst{\"a}dt et al. in Theor. Comput. Sci. 381(1-3):260-265, 2007. https://doi.org/10.1016/j.tcs.2007.04.006). The weighted case has not been considered before.},
  language  = {en}
}