{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article8616","name":"The Complexity Landscape of Fixed-Parameter Directed Steiner Network Problems (Invited Talk)","abstract":"Given a directed graph G and a list (s_1,t_1), ..., (s_k,t_k) of terminal pairs, the Directed Steiner Network problem asks for a minimum-cost subgraph of G that contains a directed s_i-> t_i path for every 1<= i <= k. Feldman and Ruhl presented an n^{O(k)} time algorithm for the problem, which shows that it is polynomial-time solvable for every fixed number k of demands. There are special cases of the problem that can be solved much more efficiently: for example, the special case Directed Steiner Tree (when we ask for paths from a root r to terminals t_1, ..., t_k) is known to be fixed-parameter tractable parameterized by the number of terminals, that is, algorithms with running time of the form f(k)*n^{O(1)} exist for the problem. On the other hand, the special case Strongly Connected Steiner Subgraph (when we ask for a path from every t_i to every other t_j) is known to be W[1]-hard parameterized by the number of terminals, hence it is unlikely to be fixed-parameter tractable. In the talk, we survey results on parameterized algorithms for special cases of Directed Steiner Network, including a recent complete classification result (joint work with Andreas Feldmann) that systematically explores the complexity landscape of directed Steiner problems to fully understand which special cases are FPT or W[1]-hard.","keywords":["Directed Steiner Tree","Directed Steiner Network","fixed-parameter tractability","dichotomy"],"author":{"@type":"Person","name":"Marx, D\u00e1niel","givenName":"D\u00e1niel","familyName":"Marx"},"position":32,"pageStart":"32:1","pageEnd":"32:1","dateCreated":"2016-06-22","datePublished":"2016-06-22","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Marx, D\u00e1niel","givenName":"D\u00e1niel","familyName":"Marx"},"copyrightYear":"2016","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.SWAT.2016.32","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6256","volumeNumber":53,"name":"15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)","dateCreated":"2016-06-22","datePublished":"2016-06-22","editor":{"@type":"Person","name":"Pagh, Rasmus","givenName":"Rasmus","familyName":"Pagh"},"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article8616","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6256"}}}