2026-07-26T16:45:05Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:9108 2024-03-06T10:43:23Z ddc:004 open_access

Brief Announcement: Characterizing Demand Graphs for (Fixed-Parameter) Shallow-Light Steiner Network Babay, Amy Dinitz, Michael Zhang, Zeyu Shallow-Light Steiner Network Fixed-Parameter Tractability We consider the Shallow-Light Steiner Network problem from a fixed-parameter perspective. Given a graph G, a distance bound L, and p pairs of vertices {(s_i,t_i)}_{i in [p]}, the objective is to find a minimum-cost subgraph G' such that s_i and t_i have distance at most L in G' (for every i in [p]). Our main result is on the fixed-parameter tractability of this problem for parameter p. We exactly characterize the demand structures that make the problem "easy", and give FPT algorithms for those cases. In all other cases, we show that the problem is W[1]-hard. We also extend our results to handle general edge lengths and costs, precisely characterizing which demands allow for good FPT approximation algorithms and which demands remain W[1]-hard even to approximate. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Amy Babay and Michael Dinitz and Zeyu Zhang 2018 Is Part Of LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2018.104 urn:nbn:de:0030-drops-91083 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.104 eng https://creativecommons.org/licenses/by/3.0/legalcode