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Parameterized Approximation Schemes for Steiner Trees with Small Number of Steiner Vertices [article]

Pavel Dvořák, Andreas Emil Feldmann, Dušan Knop, Tomáš Masařík, Tomáš Toufar, Pavel Veselý
2020 arXiv   pre-print
We further study the parameterized approximability of other variants of Steiner Tree, such as Directed Steiner Tree and Steiner Forest.  ...  In particular, on one hand Steiner Tree is known to be APX-hard, and W[2]-hard on the other, if parameterized by the number of non-terminals (Steiner vertices) in the optimum solution.  ...  Also, we thank Jiří Sgall and Martin Böhm for finding a mistake in a preliminary version of the proof of Lemma 11.  ... 
arXiv:1710.00668v4 fatcat:cgeptxhgobfg3ebkd3ul4so55e

Parameterized Study of Steiner Tree on Unit Disk Graphs

Sujoy Bhore, Paz Carmi, Sudeshna Kolay, Meirav Zehavi, Susanne Albers
2020 Scandinavian Workshop on Algorithm Theory  
We mention that the algorithmic results can be made to work for Steiner Tree on disk graphs with bounded aspect ratio.  ...  We also show that the Steiner Tree problem on unit disk graphs parameterized by k has an FPT algorithm with running time 2^{O(k)}n^{O(1)}.  ...  In [15] , Dcořák et al. designed an efficient parameterized approximation scheme (EPAS) for the Steiner Tree parameterized by k 1 .  ... 
doi:10.4230/lipics.swat.2020.13 dblp:conf/swat/BhoreCKZ20 fatcat:5hl32ecyofhj3aidc73jspmn2e

Parameterized Study of Steiner Tree on Unit Disk Graphs [article]

Sujoy Bhore, Paz Carmi, Sudeshna Kolay, Meirav Zehavi
2020 arXiv   pre-print
We mention that the algorithmic results can be made to work for the Steiner Tree on disk graphs with bounded aspect ratio.  ...  We also show that the Steiner Tree problem on unit disk graphs parameterized by k has an FPT algorithm with running time 2^O(k)n^O(1).  ...  In [15] , Dcořák et al. designed an efficient parameterized approximation scheme (EPAS) for the Steiner Tree parameterized by k 1 .  ... 
arXiv:2004.09220v1 fatcat:quagp4jzojbj5divftlmz2plke

Parameterized and Approximation Algorithms for the Steiner Arborescence Problem on a Hypercube [article]

Sugyani Mahapatra, Manikandan Narayanan, N S Narayanaswamy, Vijayaragunathan Ramamoorthi
2022 arXiv   pre-print
We study this problem with respect to three different parameters: (i) the number of terminals |R|, (ii) the optimal number of Steiner nodes (p_opt), and (iii) the penalty q := 𝙲𝙾𝚂𝚃(T) - m (while q_opt  ...  With applications in evolutionary/phylogenetic tree reconstruction algorithms and incremental algorithms for computing a property on multiple input graphs, any algorithm for this problem would open up  ...  Although parameterized approximation schemes (PAS) and polynomial size approximate kernelization schemes (PSAKS) exist for general undirected graphs when parameterized by number of terminals |R|, no polynomial  ... 
arXiv:2110.02830v3 fatcat:3kkmwubz65fm5p76q4e2gersim

The PACE 2018 Parameterized Algorithms and Computational Experiments Challenge: The Third Iteration

Édouard Bonnet, Florian Sikora, Michael Wagner
2019 International Symposium on Parameterized and Exact Computation  
This year, all three tracks were dedicated to solve the Steiner Tree problem, in which, given an edgeweighted graph and a subset of its vertices called terminals, one has to find a minimum-weight subgraph  ...  In Track A, the number of terminals was limited. In Track B, a tree-decomposition of the graph was provided in the input, and the treewidth was limited. Finally, Track C welcomed heuristics.  ...  We are particularly happy that this edition attracted many people outside the parameterized complexity community, and wish that this will continue for the future editions.  ... 
doi:10.4230/lipics.ipec.2018.26 dblp:conf/iwpec/BonnetS18 fatcat:k5mnkqudevcv5grjckenwoxjji

A Survey on Approximation in Parameterized Complexity: Hardness and Algorithms [article]

Andreas Emil Feldmann, Karthik C. S., Euiwoong Lee, Pasin Manurangsi
2020 arXiv   pre-print
Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results.  ...  We survey developments in the area both from the algorithmic and hardness perspectives, with emphasis on new techniques and potential future research directions.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
arXiv:2006.04411v1 fatcat:hjgu7f3s7zbydkcnioq3qlzgza

A Survey on Approximation in Parameterized Complexity: Hardness and Algorithms

Andreas Emil Feldmann, Karthik C. S., Euiwoong Lee, Pasin Manurangsi
2020 Algorithms  
Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results.  ...  We survey developments in the area both from the algorithmic and hardness perspectives, with emphasis on new techniques and potential future research directions.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/a13060146 fatcat:2u2vv3uksfguvj6473t2gsq42a

A Parameterized Approximation Algorithm for The Shallow-Light Steiner Tree Problem [article]

Longkun Guo, Kewen Liao
2013 arXiv   pre-print
We firstly present an exact algorithm for SLST with time complexity O(3^|S||V|D+2^|S||V|^2D^2+|V|^3D^3), where |S| and |V| are the number of terminals and vertices respectively.  ...  This is a pseudo polynomial time parameterized algorithm with respect to the parameterization: "number of terminals".  ...  [2] , polylogarithmic approximations have been developed for acyclic graph with restrained level, where level is maximal number of edges on a path of the graph.  ... 
arXiv:1212.3403v2 fatcat:we4jo3gtzvehvku7ovzbc2x7ly

Algorithms for Optimization Problems in Planar Graphs (Dagstuhl Seminar 16221)

Jeff Erickson, Philip N. Klein, Dániel Marx, Claire Mathieu, Marc Herbstritt
2016 Dagstuhl Reports  
This report contains abstracts for the recent developments in planar graph algorithms discussed during the seminar as well as summaries of open problems in this area of research.  ...  This report documents the program and the outcomes of Dagstuhl Seminar 16221 "Algorithms for Optimization Problems in Planar Graphs". The seminar was held from May 29 to June 3, 2016.  ...  Our PTAS for planar group Steiner tree implies the first PTAS for geometric Euclidean group Steiner tree with obstacles, as well as a (2 + ε)-approximation algorithm for group TSP with obstacles, improving  ... 
doi:10.4230/dagrep.6.5.94 dblp:journals/dagstuhl-reports/EricksonKMM16 fatcat:wasdfgivt5fqdppfxo3iqqs2ta

Parameterized Approximation Algorithms for Bidirected Steiner Network Problems

Rajesh Chitnis, Andreas Emil Feldmann, Pasin Manurangsi
2021 ACM Transactions on Algorithms  
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 .  ...  In light of this, we systematically study several special cases of DSN and determine their parameterized approximability for the parameter k .  ...  [31] with a recent parameterized hardness of approximation 20:10 Parameterized Approximations for Bidirected Steiner Networks result for Densest k-Subgraph [8] .  ... 
doi:10.1145/3447584 fatcat:y7fiweqxgjgwrh6wt73ri4su34

The Parameterized Complexity of the Survivable Network Design Problem [article]

Andreas Emil Feldmann, Anish Mukherjee, Erik Jan van Leeuwen
2021 arXiv   pre-print
Directed Steiner Tree (DST) problem can be seen as single-source EC-SNDP with d_max=1 on directed graphs, and is FPT parameterized by k [Dreyfus Wagner 1971].  ...  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 d_s,t for every terminal pair s,t∈ R.  ...  [6] give an approximation scheme for Steiner Forest with XP runtime parameterized by the treewidth alone. They leave open whether this can be improved to FPT runtime.  ... 
arXiv:2111.02295v1 fatcat:pckb5zxjanfhzmj7vw5gxeutxq

A Steiner tree approach to efficient object detection

Olga Russakovsky, Andrew Y. Ng
2010 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition  
At the heart of our approach is a reduction to a directed Steiner tree optimization problem, which we solve approximately in order to select the segmentation algorithm parameters.  ...  Our method uses a segmentation algorithm to select a small number of image regions on which to run a classifier.  ...  This work was supported in part by the Office of Naval Research under MURI N000140710747.  ... 
doi:10.1109/cvpr.2010.5540097 dblp:conf/cvpr/RussakovskyN10 fatcat:meiuaucswrcllpmefcg4c67kb4

Approximating Subdense Instances of Covering Problems [article]

Jean Cardinal, Marek Karpinski, Richard Schmied, Claus Viehmann
2010 arXiv   pre-print
We design new approximation algorithms as well as new polynomial time approximation schemes (PTASs) for those problems and establish first approximation hardness results for them.  ...  We study approximability of subdense instances of various covering problems on graphs, defined as instances in which the minimum or average degree is Omega(n/psi(n)) for some function psi(n)=omega(1) of  ...  There exist quasi-polynomial time approximation schemes (QPTAS) for polylog(n)-dense instances of the Steiner Tree problem.  ... 
arXiv:1011.0078v2 fatcat:uvoacc3fmnapjeosar74qqsos4

Approximating Subdense Instances of Covering Problems

Jean Cardinal, Marek Karpinski, Richard Schmied, Claus Viehmann
2011 Electronic Notes in Discrete Mathematics  
We design new approximation algorithms as well as new polynomial time approximation schemes (PTASs) for those problems and establish first approximation hardness results for them.  ...  We study approximability of subdense instances of various covering problems on graphs, defined as instances in which the minimum or average degree is Ω(n/ψ(n)) for some function ψ(n) = ω(1) of the instance  ...  There exist quasi-polynomial time approximation schemes (QPTAS) for polylog(n)-dense instances of the Steiner Tree problem.  ... 
doi:10.1016/j.endm.2011.05.051 fatcat:ejhiknoqhvcgjhjfisetpr4lqq

A parallel Steiner tree heuristic for macro cell routing

Christian Fobel, Gary Grewal
2008 2008 IEEE International Conference on Computer Design  
Steiner trees for each net that must be routed.  ...  Macro cells are large, irregularly sized parameterized circuit modules that typically contain large numbers of terminals that must be interconnected.  ...  If the capacity constraints of some edges cannot be satisfied, routes must be ripped up and then rerouted using alternate Steiner trees compatible with the Steiner trees used for connecting other nets.  ... 
doi:10.1109/iccd.2008.4751836 dblp:conf/iccd/FobelG08 fatcat:jjvgnnakjbemjiouzc3hrjd3k4
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