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The Parameterized Complexity of the Survivable Network Design Problem

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10453269" target="_blank" >RIV/00216208:11320/22:10453269 - isvavai.cz</a>

  • Result on the web

    <a href="https://doi.org/10.1137/1.9781611977066.4" target="_blank" >https://doi.org/10.1137/1.9781611977066.4</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1137/1.9781611977066.4" target="_blank" >10.1137/1.9781611977066.4</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    The Parameterized Complexity of the Survivable Network Design Problem

  • Original language description

    For the well-known Survivable Network Design Problem (SNDP) we are given an undirected graph G with edge costs, a set R of terminal vertices, and an integer demand ds,t for every terminal pair s,tELEMENT OFR. The task is to compute a subgraph H of G of minimum cost, such that there are at least ds,t disjoint paths between s and t in H. If the paths are required to be edge-disjoint we obtain the edge-connectivity variant (EC-SNDP), while internally vertex-disjoint paths result in the vertex-connectivity variant (VC-SNDP). Another important case is the element-connectivity variant (LC-SNDP), where the paths are disjoint on edges and non-terminals.In this work we shed light on the parameterized complexity of the above problems. We consider several natural parameters, which include the solution size ℓ, the sum of demands D, the number of terminals k, and the maximum demand dmax. Using simple, elegant arguments, we prove the following results.- We give a complete picture of the parameterized tractability of the three variants w.r.t. parameter ℓ: both EC-SNDP and LC-SNDP are FPT, while VC-SNDP is W[1]-hard.- We identify some special cases of VC-SNDP that are FPT:* when dmax&lt;=3 for parameter ℓ,* on locally bounded treewidth graphs (e.g., planar graphs) for parameter ℓ, and* on graphs of treewidth tw for parameter tw+D.- The well-known Directed Steiner Tree (DST) problem can be seen as single-source EC-SNDP with dmax=1 on directed graphs, and is FPT parameterized by k [Dreyfus &amp; Wagner 1971]. We show that in contrast, the 2-DST problem, where dmax=2, is W[1]-hard, even when parameterized by ℓ.

  • Czech name

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

  • OECD FORD branch

    10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Result continuities

  • Project

    <a href="/en/project/GX19-27871X" target="_blank" >GX19-27871X: Efficient approximation algorithms and circuit complexity</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Others

  • Publication year

    2022

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Article name in the collection

    5th Symposium on Simplicity in Algorithms

  • ISBN

    978-1-61197-706-6

  • ISSN

  • e-ISSN

  • Number of pages

    20

  • Pages from-to

    37-56

  • Publisher name

    Society for Industrial and Applied Mathematics

  • Place of publication

    Alexandria, US

  • Event location

    virtual

  • Event date

    Jan 10, 2022

  • Type of event by nationality

    WRD - Celosvětová akce

  • UT code for WoS article