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O(1) Steiner Point Removal in Series-Parallel Graphs

Authors D. Ellis Hershkowitz, Jason Li

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Author Details

D. Ellis Hershkowitz
  • Carnegie Mellon University, Pittsburgh, PA, USA
Jason Li
  • Berkeley, CA, USA

Funding

Supported in part by NSF grants CCF-1527110, CCF-1618280, CCF-1814603, CCF-1910588, NSF CAREER award CCF-1750808, a Sloan Research Fellowship, funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (ERC grant agreement 949272) and Swiss National Foundation (project grant 200021-184735).
  • Hershkowitz, D. Ellis: Supported by the Air Force Office of Scientific Research under award number FA9550-20-1-0080.

Cite As Get BibTex

D. Ellis Hershkowitz and Jason Li. O(1) Steiner Point Removal in Series-Parallel Graphs. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 66:1-66:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.ESA.2022.66

Abstract

We study how to vertex-sparsify a graph while preserving both the graph’s metric and structure. Specifically, we study the Steiner point removal (SPR) problem where we are given a weighted graph G = (V,E,w) and terminal set V' ⊆ V and must compute a weighted minor G' = (V',E', w') of G which approximates G’s metric on V'. A major open question in the area of metric embeddings is the existence of O(1) multiplicative distortion SPR solutions for every (non-trivial) minor-closed family of graphs. To this end prior work has studied SPR on trees, cactus and outerplanar graphs and showed that in these graphs such a minor exists with O(1) distortion.
We give O(1) distortion SPR solutions for series-parallel graphs, extending the frontier of this line of work. The main engine of our approach is a new metric decomposition for series-parallel graphs which we call a hammock decomposition. Roughly, a hammock decomposition is a forest-like structure that preserves certain critical parts of the metric induced by a series-parallel graph.

Subject Classification

ACM Subject Classification
  • Theory of computation → Sparsification and spanners
  • Theory of computation → Shortest paths
  • Theory of computation → Approximation algorithms analysis
Keywords
  • Metric embeddings
  • graph algorithms
  • vertex sparsification

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