Corpus ID: 237532772

Retraction: Improved Approximation Schemes for Dominating Set Problems in Unit Disk Graphs

@article{Fakcharoenphol2021RetractionIA,
  title={Retraction: Improved Approximation Schemes for Dominating Set Problems in Unit Disk Graphs},
  author={Jittat Fakcharoenphol and Pattara Sukprasert},
  journal={ArXiv},
  year={2021},
  volume={abs/2109.01283}
}
Retraction note: After posting the manuscript on arXiv, we were informed by Erik Jan van Leeuwen that both results were known and they appeared in his thesis [vL09]. A PTAS for MDS is at Theorem 6.3.21 on page 79 and A PTAS for MCDS is at Theorem 6.3.31 on page 82. The techniques used are very similar. He noted that the idea for dealing with the connected version using a constant number of extra layers in the shifting technique not only appeared Zhang et al [ZGWD09] but also in his 2005 paper… Expand

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References

SHOWING 1-10 OF 28 REFERENCES
Local PTAS for Dominating and Connected Dominating Set in Location Aware Unit Disk Graphs
TLDR
It is shown that the processing time that each vertex needs to determine whether or not it is part of the computed set is bounded by a polynomial in the number of vertices which are a constant number of hops away from it. Expand
A PTAS for the Minimum Dominating Set Problem in Unit Disk Graphs
TLDR
The proposed polynomial-time approximation scheme, the PTAS, accepts any undirected graph as input, and returns a (1+e)-approximate minimum dominating set, or a certificate showing that the input graph is no unit disk graph, making the algorithm robust. Expand
Approximation algorithms for NP-complete problems on planar graphs
  • B. Baker
  • Mathematics, Computer Science
  • 24th Annual Symposium on Foundations of Computer Science (sfcs 1983)
  • 1983
TLDR
A general technique that can be used to obtain approximation algorithms for various NP-complete problems on planar graphs, which includes maximum independent set, maximum tile salvage, partition into triangles, maximum H-matching, minimum vertex cover, minimum dominating set, and minimum edge dominating set. Expand
Connected Dominating Set: Theory and Applications
TLDR
This book is going to collect recent developments on the connected dominating set, which presents the state of the art in the study of connected dominating sets and includes motivation and overview, problem complexity analysis, and approximation algorithm designs. Expand
PTAS for the minimum weighted dominating set in growth bounded graphs
TLDR
This paper presents a PTAS for MWDS in polynomial growth bounded graphs with bounded degree constraint using the local neighborhood-based scheme technique. Expand
Approximation Algorithms for Unit Disk Graphs
TLDR
A new asymptotic fully-polynomial approximation scheme for unit disk graphs of bounded density is presented, and the scheme for Minimum Connected Dominating Set is the first Baker-like asymPTotic FPTAS for this problem. Expand
On the Optimality of Planar and Geometric Approximation Schemes
  • D. Marx
  • Mathematics, Computer Science
  • 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)
  • 2007
TLDR
For several planar and geometric problems that the best known approximation schemes are essentially optimal with respect to the dependence on epsi, it is shown that if there is a delta 0 such that any of these problems admits a 2-delta O(1/epsi), then ETH fails. Expand
NC-Approximation Schemes for NP- and PSPACE-Hard Problems for Geometric Graphs
TLDR
The approximation schemes for hierarchically specified unit disk graphs presented in this paper are among the first approximation schemes in the literature for natural PSPACE-hard optimization problems. Expand
New approximations for minimum-weighted dominating sets and minimum-weighted connected dominating sets on unit disk graphs
TLDR
This paper proposes a (4 +@e)-approximation algorithm for an MWDS based on a dynamic programming algorithm for a Min-Weight Chromatic Disk Cover and shows a polynomial-time approximation scheme for a Node-Weighted Steiner Tree problem when the given terminal set is c-local. Expand
Approximation schemes for covering and packing problems in image processing and VLSI
TLDR
The unified technique that is introduced here, referred to as the shifting strategy, is applicable to numerous geometric covering and packing problems and how it varies with problem parameters is illustrated. Expand
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