Brief Announcement: Characterizing Demand Graphs for (Fixed-Parameter) Shallow-Light Steiner Network

Authors Amy Babay, Michael Dinitz, Zeyu Zhang

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Amy Babay
  • Johns Hopkins University, Baltimore, MD, USA
Michael Dinitz
  • Johns Hopkins University, Baltimore, MD, USA
Zeyu Zhang
  • Johns Hopkins University, Baltimore, MD, USA

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Amy Babay, Michael Dinitz, and Zeyu Zhang. Brief Announcement: Characterizing Demand Graphs for (Fixed-Parameter) Shallow-Light Steiner Network. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 104:1-104:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Shallow-Light
  • Steiner Network
  • Fixed-Parameter Tractability


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