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What can be approximated locally?
2008
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures - SPAA '08
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In this technical report, we present the first 1 distributed algorithm approximating a minimum dominating set on a planar graph within a constant factor in constant time. ...
Whether local algorithms can compute constant approximations of NP-hard problems is of both practical and theoretical interest. ...
We present a constant-time constant-approximation local algorithm for the minimum dominating set problem on planar graphs (shown to be NP-complete in [11] ). ...
doi:10.1145/1378533.1378540
dblp:conf/spaa/LenzenOW08
fatcat:2htcpa6mfndwfajjzlxpiapam4
Linear-Time Computation of a Linear Problem Kernel for Dominating Set on Planar Graphs
[chapter]
2012
Lecture Notes in Computer Science
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In addition, a minimum dominating set for G can be inferred from a minimum dominating set for G . ...
In terms of parameterized algorithmics, this implies a linear-size problem kernel for the NP-hard Dominating Set problem on planar graphs, where the kernelization takes linear time. ...
Conclusion Our work is meant to provide a first case study, using the well-known kernelization of Dominating Set on planar graphs, on how known kernelization algorithms can be tuned for better time performance ...
doi:10.1007/978-3-642-28050-4_16
fatcat:cvbceyuhu5crnjtfyrt5v7mstm
Survey of local algorithms
2013
ACM Computing Surveys
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When we study local algorithms, we assume that the problem instance is given in a distributed manner: each node in the communication graph G knows part of the input. ...
Being highly scalable and fault-tolerant, such algorithms are ideal in the operation of large-scale distributed systems. ...
Acknowledgements This is the author's version of the work; the definitive version will be published in ACM Computing Surveys [136] . ...
doi:10.1145/2431211.2431223
fatcat:zlnxn57wunh6jl5om2lagbfvim
A local constant-factor approximation algorithm for MDS problem in anonymous network
[article]
2013
arXiv
pre-print
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One of the open issues was whether identifiers are essential in planar graphs. ...
In research on distributed local algorithms it is commonly assumed that each vertex has a unique identifier in the entire graph. ...
Lemma 4 . 4 Let G = (V, E) be a graph and M be a dominating set in G. ...
arXiv:1303.2514v2
fatcat:vfh224jdl5f5dl3vd5f7nd5gmy
Dominating Sets and Local Treewidth
[chapter]
2003
Lecture Notes in Computer Science
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An interesting question motivating our study is if similar bounds can be obtained for larger minor closed graph families. ...
It is known that the treewidth of a planar graph with a dominating set of size d is O( √ d) and this fact is used as the basis for several fixed parameter algorithms on planar graphs. ...
Also the classical Baker's technique [4] for obtaining approximation schemes on planar graphs for different NP hard problems can be generalized to minor closed families of bounded local treewidth. ...
doi:10.1007/978-3-540-39658-1_22
fatcat:bknu63go7fhgvh2ab6jmfqdowe
Local solutions for global problems in wireless networks
2007
Journal of Discrete Algorithms
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We review algorithms for obtaining planar subnetworks, approximations to minimum weight spanning trees, Delaunay triangulations, and relative neighbor graphs. ...
Given a unit distance wireless network N , we present new local algorithms to solve the following problems: 1. Calculate small dominating sets (not necessarily connected) of N . 2. ...
general we can expect RNG graphs to be good approximations to MWST . ...
doi:10.1016/j.jda.2006.05.004
fatcat:ymqkmdsitbcinnffhijc3thijq
Optimality of Geometric Local Search
2018
International Symposium on Computational Geometry
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We show that in fact the approximation guarantee of local search cannot be improved for any of these problems. ...
This included the existence of polynomial-time approximation schemes (PTASs) for hitting set, set cover, dominating set, independent set, and other problems for some basic geometric objects. ...
Introduction Within the past decade polynomial-time approximation schemes (PTASs) have been proposed for a number of long-standing open problems in geometric approximation algorithms, including the following ...
doi:10.4230/lipics.socg.2018.48
dblp:conf/compgeom/JartouxM18
fatcat:xypsadjajnbzhgiigaw2w5ffxm
Fast Algorithms for Hard Graph Problems: Bidimensionality, Minors, and Local Treewidth
[chapter]
2005
Lecture Notes in Computer Science
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This paper surveys the theory of bidimensional graph problems. ...
We summarize the known combinatorial and algorithmic results of this theory, the foundational Graph Minor results on which this theory is based, and the remaining open problems. ...
We thank Fedor Fomin, Naomi Nishimura, Prabhakar Ragde, Paul Seymour, and Dimitrios Thilikos for their fruitful collaboration and discussions in this area. ...
doi:10.1007/978-3-540-31843-9_57
fatcat:bl5d75gm7nechmehbwv2blc33m
Local Algorithms: Self-stabilization on Speed
[chapter]
2009
Lecture Notes in Computer Science
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This work was supported in part by the Academy of Finland, Grant 116547, by Helsinki Graduate School in Computer Science and Engineering (Hecse), and by the Foundation of Nokia Corporation. ...
For example, in the case of the minimum dominating set problem, we can study the LP relaxation of the problem. ...
As the maximum independent set problem is hard to approximate even in a centralized setting, we focus on the special case of planar graphs. Czygrinow et al. ...
doi:10.1007/978-3-642-05118-0_2
fatcat:tp3fdm4hzvcjdjgbqxbeuaqwmy
Local Solid Shape
2015
i-Perception
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This should be distinguished from local shape in pictorial space. The difference is categorical. ...
Local solid shape applies to the surface curvature of small surface patches-essentially regions of approximately constant curvatures-of volumetric objects that are smooth volumetric regions in Euclidean ...
Of course, the planar case is singular, occurring with probability zero. 5 We will ignore it in this study. ...
doi:10.1177/2041669515604063
pmid:27648217
pmcid:PMC5016822
fatcat:gtb4l7jywjhxvbwys5mvn72yhi
Centroidal Localization Game
2018
Electronic Journal of Combinatorics
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Let $\zeta^* (G)$ be the minimum $k$ such that the entity is eventually located, whatever it does, in the graph $G$. ...
In a more realistic setting, each device does not get the exact distance to the entity's location. ...
Finally, we ask what happens if the Cop-player is given a set of vertices S ⊂ V (G) such that she can only choose vertices from this set, meaning in each round C ⊂ S. ...
doi:10.37236/7488
fatcat:qli2oz6kmzdblpeyjdrtbxediy
Lower bounds for local approximation
2012
Proceedings of the 2012 ACM symposium on Principles of distributed computing - PODC '12
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same approximation ratio can be achieved on anonymous networks. ...
, dominating sets, and edge dominating sets. ...
This work was supported in part by the Academy of Finland, Grants 132380 and 252018, the Research Funds of the University of Helsinki, and the Finnish Cultural Foundation. ...
doi:10.1145/2332432.2332465
dblp:conf/podc/GoosHS12
fatcat:wppjy42vzjep7fexqffdztwucm
Local search: Is brute-force avoidable?
2012
Journal of computer and system sciences (Print)
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Many local search algorithms are based on searching in the k-exchange neighborhood. This is the set of solutions that can be obtained from the current solution by exchanging at most k elements. ...
In particular, on planar graphs, all our algorithms searching for a k-local improvement run in time O(2 O(k) · n 2 ), which is polynomial for k = O(log n). ...
This is the case for the problems Vertex Cover, Independent Set, Dominating Set, Edge Dominating Set, and Minimum Maximal Matching, to name a few that we explore in this paper. ...
doi:10.1016/j.jcss.2011.10.003
fatcat:t5j76ca5yfc4zo6ljy5ovstquq
Lower bounds for local approximation
2013
Journal of the ACM
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same approximation ratio can be achieved on anonymous networks. ...
, dominating sets, and edge dominating sets. ...
This work was supported in part by the Academy of Finland, Grants 132380 and 252018, the Research Funds of the University of Helsinki, and the Finnish Cultural Foundation. ...
doi:10.1145/2528405
fatcat:o4haippqu5hqhfzeeomxtsy7va
Centroidal localization game
[article]
2018
arXiv
pre-print
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Let ζ^* (G) be the minimum k such that the entity is eventually located, whatever it does, in the graph G. ...
The centroidal dimension of a graph G is the minimum number of devices required to locate the entity in this setting. ...
Recall that a dominating set D ⊆ V of a graph G = (V, E) is a set such that any vertex of V is in the closed neighborhood of some vertex of D. ...
arXiv:1711.08836v2
fatcat:x6jeq37v35a77dnxi3lmxvfnwa
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