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A New Approach for Approximating Directed Rooted Networks

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Graph-Theoretic Concepts in Computer Science (WG 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14760))

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Abstract

We consider the k-outconnected directed Steiner tree problem (k-DST). Given a directed edge-weighted graph \(G=(V,E,w)\), where \(V = \{r\} \cup S \cup T\), and an integer k, the goal is to find a minimum cost subgraph of G in which there are k edge-disjoint rt-paths for every terminal \(t \in T\). The problem is known to be NP-Hard. Furthermore, the question on whether a polynomial time, subpolynomial approximation algorithm exists for k-DST was answered negatively by Grandoni et al. (2018), by proving an approximation hardness of \(\Omega (|T|/\log |T|)\) under NP\(\ne \)ZPP.

Inspired by modern day applications, we focus on developing efficient algorithms for k-DST in graphs where terminals have out-degree 0, and furthermore constitute the vast majority in the graph. We provide the first approximation algorithm for k-DST on such graphs, in which the approximation ratio depends (primarily) on the size of S. We present a randomized algorithm that finds a solution of weight at most \(O(k|S| \log |T|)\) times the optimal weight, and with high probability runs in polynomial time.

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Authors and Affiliations

  1. The Academic College of Tel Aviv-Yaffo, Tel Aviv, Israel

    Sarel Cohen & Lior Kamma

  2. Hasso Plattner Institute, University of Potsdam, Potsdam, Germany

    Aikaterini Niklanovits

Authors
  1. Sarel Cohen
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  2. Lior Kamma
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  3. Aikaterini Niklanovits
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Correspondence to Lior Kamma .

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Editors and Affiliations

  1. Masaryk University, Brno, Czech Republic

    Daniel Kráľ

  2. University of Primorska, Koper, Slovenia

    Martin Milanič

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Cohen, S., Kamma, L., Niklanovits, A. (2025). A New Approach for Approximating Directed Rooted Networks. In: Kráľ, D., Milanič, M. (eds) Graph-Theoretic Concepts in Computer Science. WG 2024. Lecture Notes in Computer Science, vol 14760. Springer, Cham. https://doi.org/10.1007/978-3-031-75409-8_11

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  • DOI: https://doi.org/10.1007/978-3-031-75409-8_11

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