2026-08-07T09:49:36Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:18838 2024-03-06T11:02:42Z ddc:004 open_access

A Constant-Factor Approximation for Quasi-Bipartite Directed Steiner Tree on Minor-Free Graphs Friggstad, Zachary Mousavi, Ramin Directed Steiner tree Combinatorial optimization approximation algorithms We give the first constant-factor approximation algorithm for quasi-bipartite instances of Directed Steiner Tree on graphs that exclude fixed minors. In particular, for K_r-minor-free graphs our approximation guarantee is O(r⋅√(log r)) and, further, for planar graphs our approximation guarantee is 20. Our algorithm uses the primal-dual scheme. We employ a more involved method of determining when to buy an edge while raising dual variables since, as we show, the natural primal-dual scheme fails to raise enough dual value to pay for the purchased solution. As a consequence, we also demonstrate integrality gap upper bounds on the standard cut-based linear programming relaxation for the Directed Steiner Tree instances we consider. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Zachary Friggstad and Ramin Mousavi 2023 Is Part Of LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX/RANDOM.2023.13 urn:nbn:de:0030-drops-188389 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.13 eng https://creativecommons.org/licenses/by/4.0/legalcode