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An FPT Algorithm for Minimum Additive Spanner Problem

Author Yusuke Kobayashi

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Yusuke Kobayashi
  • Research Institute for Mathematical Sciences, Kyoto University, Japan

Funding

  • Kobayashi, Yusuke: Supported by JST ACT-I Grant Number JPMJPR17UB, and JSPS KAKENHI Grant Numbers JP16K16010, 16H03118, JP18H05291, and JP19H05485, Japan.

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Yusuke Kobayashi. An FPT Algorithm for Minimum Additive Spanner Problem. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 11:1-11:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.STACS.2020.11

Abstract

For a positive integer t and a graph G, an additive t-spanner of G is a spanning subgraph in which the distance between every pair of vertices is at most the original distance plus t. The Minimum Additive t-Spanner Problem is to find an additive t-spanner with the minimum number of edges in a given graph, which is known to be NP-hard. Since we need to care about global properties of graphs when we deal with additive t-spanners, the Minimum Additive t-Spanner Problem is hard to handle and hence only few results are known for it. In this paper, we study the Minimum Additive t-Spanner Problem from the viewpoint of parameterized complexity. We formulate a parameterized version of the problem in which the number of removed edges is regarded as a parameter, and give a fixed-parameter algorithm for it. We also extend our result to the case with both a multiplicative approximation factor α and an additive approximation parameter β, which we call (α, β)-spanners.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
Keywords
  • Graph algorithms
  • Fixed-parameter tractability
  • Graph spanner

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