Parameterized Approximation Algorithms for Bidirected Steiner Network Problems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10437394" target="_blank" >RIV/00216208:11320/21:10437394 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=a.QxLFrQ_e" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=a.QxLFrQ_e</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1145/3447584" target="_blank" >10.1145/3447584</a>
Alternative languages
Result language
angličtina
Original language name
Parameterized Approximation Algorithms for Bidirected Steiner Network Problems
Original language description
The Directed Steiner Network (DSN) problem takes as input a directed graph G = (V, E) with non-negative edge-weights and a set D subset of V x V of k demand pairs. The aim is to compute the cheapest network N subset of G for which there is an s -> t path for each (s, t) is an element of D. It is known that this problem is notoriously hard, as there is no k(1/4-o(1))-approximation algorithm under Gap-ETH, even when parametrizing the runtime by k [Dinur & Manurangsi, ITCS 2018]. In light of this, we systematically study several special cases of DSN and determine their parameterized approximability for the parameter k. For the bi-DSNPLANAR problem, the aim is to compute a solution N subset of G whose cost is at most that of an optimum planar solution in a bidirected graph G, i.e., for every edge uv of G the reverse edge vu exists and has the same weight. This problem is a generalization of several well-studied special cases. Our main result is that this problem admits a parameterized approximation scheme (PAS) for k. We also prove that our result is tight in the sense that (a) the runtime of our PAS cannot be significantly improved, and (b) no PAS exists for any generalization of bi-DSNPLANAR, under standard complexity assumptions. The techniques we use also imply a polynomial-sized approximate kernelization scheme (PSAKS). Additionally, we study several generalizations of bi-DSNPLANAR and obtain upper and lower bounds on obtainable runtimes parameterized by k. One important special case of DSN is the Strongly CONNECTED STEINER Subgraph (SCSS) problem, for which the solution network N subset of G needs to strongly connect a given set of k terminals. It has been observed before that for SCSS a parameterized 2-approximation exists for parameter k [Chitnis et al., IPEC 2013]. We give a tight inapproximability result by showing that for k no parameterized (2 - epsilon)-approximation algorithm exists under Gap-ETH. Additionally, we show that when restricting the input of SCSS to bidirected graphs, the problem remains NP-hard but becomes FPT for k.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
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
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
ACM Transactions on Algorithms
ISSN
1549-6325
e-ISSN
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Volume of the periodical
17
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
68
Pages from-to
12
UT code for WoS article
000661311300002
EID of the result in the Scopus database
2-s2.0-85107813086