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Improved Algorithms and Complexity Results for Power Domination in Graphs

2007
*
Algorithmica
*

The Power

doi:10.1007/s00453-007-9147-x
fatcat:prp3jqhg6rhf7pr63iw7ns6c5e
*Dominating**Set*problem is a variant of the classical*domination*problem*in**graphs*: Given an undirected*graph*G = (V, E), find a minimum P ⊆ V such that all vertices*in*V are "observed" by vertices ... Moreover, we simplify*and*extend several NP-completeness results, particularly showing that Power*Dominating**Set*remains NP-complete for planar*graphs*, for circle*graphs*,*and*for split*graphs*. ... For a vertex v*in**graph*G, we denote by N G (v) the*open**neighborhood*of v*in*G. By N G [v] , we refer to the closed*neighborhood*of v. ...##
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Improved Algorithms and Complexity Results for Power Domination in Graphs
[chapter]

2005
*
Lecture Notes in Computer Science
*

The Power

doi:10.1007/11537311_16
fatcat:tgri7qpg55ff3ik5zprjpao3hy
*Dominating**Set*problem is a variant of the classical*domination*problem*in**graphs*: Given an undirected*graph*G = (V, E), find a minimum P ⊆ V such that all vertices*in*V are "observed" by vertices ... Moreover, we simplify*and*extend several NP-completeness results, particularly showing that Power*Dominating**Set*remains NP-complete for planar*graphs*, for circle*graphs*,*and*for split*graphs*. ... For a vertex v*in**graph*G, we denote by N G (v) the*open**neighborhood*of v*in*G. By N G [v] , we refer to the closed*neighborhood*of v. ...##
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Fatgraph Algorithms and the Homology of the Kontsevich Complex
[article]

2012
*
arXiv
*
pre-print

This paper presents

arXiv:1202.1820v2
fatcat:uogtfb7i5jamxiw63gt5q2pjve
*algorithms*to: (1) generate the*set*of all fatgraphs having a given genus*and*number of boundary cycles; (2) compute automorphisms of any given fatgraph; (3) compute the homology of ... the fatgraph*complex*. ... (*and*particularly the "Theoretical Chemistry*and*Computational Grid Applications" research group led by Kim Baldridge), whose support is here gratefully acknowledged. ...##
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Partial Domination in Graphs
[article]

2017
*
arXiv
*
pre-print

*In*this paper we propose relaxing this requirement, by seeking

*sets*of vertices that

*dominate*a prescribed fraction of the vertices of a

*graph*. ... A

*set*S⊆ V is a

*dominating*

*set*of G if every vertex

*in*V - S is adjacent to at least one vertex

*in*S. ... We conclude our look at computational

*complexity*by noting an interesting

*open*question.

*Open*Question 2. ...

##
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RAINBOW DOMINATION IN GRAPHS

2008
*
Taiwanese journal of mathematics
*

If we require that each vertex to which an empty

doi:10.11650/twjm/1500602498
fatcat:arkaotf2aras5fmvtlpf4lyocq
*set*is assigned has*in*its*neighborhood*all k colors, then this is called the k-rainbow*dominating*function of a*graph*G. ...*In*this paper we connect this new concept to usual*domination**in*(products of)*graphs*,*and*present its application to paired-*domination*of Cartesian products of*graphs*. ... For any vertex v ∈ V , the*open**neighborhood*of v is the*set*N (v) = {u ∈ V | uv ∈ E},*and*its closed*neighborhood*is the*set*N [v] = N (v) ∪ {v}. ...##
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Boolean operations on 3D selective Nef complexes: Data structure, algorithms, optimized implementation and experiments

2007
*
Computational geometry
*

*In*consequence, they can represent non-manifold situations,

*open*

*and*closed

*sets*, mixed-dimensional

*complexes*,

*and*they are closed under all boolean

*and*topological operations, such as complement

*and*boundary ... The implementation was released as

*Open*Source

*in*the Computational Geometry

*Algorithm*Library (CGAL) release 3.1

*in*December 2004. ...

*and*Surfaces). ...

##
###
Conflict-Free Coloring of Graphs

2018
*
SIAM Journal on Discrete Mathematics
*

We thank Bruno Crepaldi, Pedro de Rezende, Cid de Souza, Stephan Friedrichs, Michael Hemmer,

doi:10.1137/17m1146579
fatcat:uj3b7rzgsbgb3io4j7njd2i6dy
*and*Frank Quedenfeld for helpful discussions. ... Moreover, Corollary 5.1 discusses the*complexity*of k-Conflict-Free*Dominating**Set*,*and*Theorem 5.2 states positive results for outerplanar*graphs*. Theorem 5.2. ... Kikuno, Yoshida,*and*Kakuda [23] present a linear time*algorithm*for finding a minimum*dominating**set**in*a series-parallel*graph*, which includes outerplanar*graphs*. ...##
###
Biclique-Helly Graphs

2007
*
Graphs and Combinatorics
*

*In*addition, we relate biclique-Helly

*graphs*to the classes of clique-Helly, disk-Helly

*and*

*neighborhood*-Helly

*graphs*. ... A

*graph*is biclique-Helly when its family of (maximal) bicliques is a Helly family. We describe characterizations for biclique-Helly

*graphs*, leading to polynomial time recognition

*algorithms*. ...

*In*particular, he suggested the present version of the proof of Lemma 1, which is shorter

*and*more elegant than the authors' previous proof. ...

##
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Graph Isomorphism for unit square graphs
[article]

2016
*
arXiv
*
pre-print

*In*the past decades for more

*and*more

*graph*classes the

*Graph*Isomorphism Problem was shown to be solvable

*in*polynomial time. ... Using group theoretic

*algorithms*we obtain sufficient information to solve the isomorphism problem for unit square

*graphs*. ... Acknowledgements I want to thank Martin Grohe

*and*Pascal Schweitzer for several helpful discussions

*and*comments throughout this work. ...

##
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The complexity of secure domination problem in graphs

2018
*
Discussiones Mathematicae Graph Theory
*

*In*this paper, we first show that the decision version of the secure

*domination*problem is NP-complete for star convex bipartite

*graphs*

*and*doubly chordal

*graphs*. ... A

*dominating*

*set*of a

*graph*G is a subset D ⊆ V (G) such that every vertex not

*in*D is adjacent to at least one vertex

*in*D. ... Acknowledgments The authors are grateful to the referees for their valuable comments, which result

*in*the present version of the paper. This work was supported by the Natural ...

##
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Relative neighborhood graphs and their relatives

1992
*
Proceedings of the IEEE
*

This is a survey of results on

doi:10.1109/5.163414
fatcat:ddkulebyjjb5rpypvpecdvtske
*neighborhood**graphs*. The paper discusses properties, bounds on the size,*algorithms*,*and*variants of the*neighborhood**graphs*. ... Numerous applications including computational morphology, spatial analysis, pattern classification,*and*data bases for computer vision are described. ... Senn for her professional help*in**locating*many of the references. ...##
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Efficient sub-5 approximations for minimum dominating sets in unit disk graphs

2014
*
Theoretical Computer Science
*

A unit disk

doi:10.1016/j.tcs.2014.01.023
fatcat:rbqmky6winh63kh5uj7fbnpn6y
*graph*is the intersection*graph*of n congruent disks*in*the plane.*Dominating**sets**in*unit disk*graphs*are widely studied due to their application*in*wireless ad-hoc networks. ... Because the minimum*dominating**set*problem for unit disk*graphs*is NP-hard, numerous approximation*algorithms*have been proposed*in*the literature, including some PTAS. ... Conclusion*and**open*problems We introduced novel efficient*algorithms*for approximating the minimum*dominating**set**and*minimum independent*dominating**set**in*unit disk*graphs*. ...##
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An Overview of Topology Mapping Algorithms and Techniques in High-Performance Computing
[chapter]

2014
*
High-Performance Computing on Complex Environments
*

The chapter concludes by listing a series of

doi:10.1002/9781118711897.ch5
fatcat:7ok2xcxah5ctvjkuwvmaerbwgu
*open*issues*and*problems. Introduction High Performance Computing (HPC) applications are increasingly demanding*in*terms of computing power. ... Currently, this computing power can be delivered by High-Performance Computing on*Complex*Environments, First edition. By Edited by Emmanuel Jeannot*and*JuliusŽilinskas. ... Acknowledgments This work is supported by the COST Action IC0805 "*Open*European Network for High Performance Computing on*Complex*Environments". Bibliography ...##
###
Graph classes between parity and distance-hereditary graphs

1999
*
Discrete Applied Mathematics
*

Several

doi:10.1016/s0166-218x(99)00075-x
fatcat:c3k4ab62tzbsfoe7hw7nk7lksa
*graph*problems (e.g., steiner tree, connected*domination*, hamiltonian path,*and*isomorphism problem), which can be solved*in*polynomial time for distance-hereditary*graphs*, are NP-complete or*open*... To this purpose we characterize these classes using Cunningham decomposition*and*then use the devised structural characterization*in*order to show efficient*algorithms*for the recognition*and*isomorphism ... By N T (S) we denote the*neighborhood*of S*in*T , that is, the*set*of vertices*in*T that are adjacent to some vertex*in*S,*and*by N T [S] = N T (S) ∪ S the closed*neighborhood*of S*in*T . ...##
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Performance introspection of graph databases

2013
*
Proceedings of the 6th International Systems and Storage Conference on - SYSTOR '13
*

The explosion of

doi:10.1145/2485732.2485750
dblp:conf/systor/MackoMS13
fatcat:lvrid5ycpnawhnuslz7feqc3ue
*graph*data*in*social*and*biological networks, recommendation systems, provenance databases, etc. makes*graph*storage*and*processing of paramount importance. ... The suite has three layers of benchmarks: primitive operations, composite access patterns,*and**graph**algorithms*. ... We would like to thank Sparsity Technologies for providing us with a DEX license,*and*Dàmaris Coll Jimenez*and*Sergio Gómez Villamor*in*particular for helping us configure the database*and*interpret our ...
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