The Parameterized Complexity of the Survivable Network Design Problem

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

The Parameterized Complexity of the Survivable Network Design Problem

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

The Parameterized Complexity of the Survivable Network Design Problem

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

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

Projekt

<a href="/cs/project/GX19-27871X" target="_blank" >GX19-27871X: Efektivní aproximační algoritmy a obvodová složitost</a><br>

Návaznosti

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

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název statě ve sborníku

5th Symposium on Simplicity in Algorithms

ISBN

978-1-61197-706-6

ISSN

—

e-ISSN

—

Počet stran výsledku

20

Strana od-do

37-56

Název nakladatele

Society for Industrial and Applied Mathematics

Místo vydání

Alexandria, US

Místo konání akce

virtual

Datum konání akce

10. 1. 2022

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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