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<=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 & 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
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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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
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e-ISSN
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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
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