Filters








4,549,998 Hits in 4.6 sec

Dominating Sets and Connected Dominating Sets in Dynamic Graphs [article]

Niklas Hjuler, Giuseppe F. Italiano, Nikos Parotsidis, David Saulpic
2019 arXiv   pre-print
In this paper we study the dynamic versions of two basic graph problems: Minimum Dominating Set and its variant Minimum Connected Dominating Set.  ...  As a further application of our approach, we also present an algorithm that maintains a Minimal Dominating Set in O(min(Δ, √(m))) per update.  ...  The algorithm must find a new vertex to dominate u: we simply add u to the dominating set.  ... 
arXiv:1901.09877v1 fatcat:oveklp63cvccnhnrzo4ujdjdli

Dominating Sets and Connected Dominating Sets in Dynamic Graphs

Niklas Hjuler, Giuseppe F. Italiano, Nikos Parotsidis, David Saulpic, Michael Wagner
2019 Symposium on Theoretical Aspects of Computer Science  
In this paper we study the dynamic versions of two basic graph problems: Minimum Dominating Set and its variant Minimum Connected Dominating Set.  ...  As a further application of our approach, we also present an algorithm that maintains a Minimal Dominating Set in O(min(∆, √ m )) per update.  ...  A O(min(∆, √ m) ) amortized algorithm for Minimal Dominating Set 35:15 for some vertex w and OnlyBy(w) = {u}: in other terms, u was dominated only by w, and w was in the dominating set only to dominate  ... 
doi:10.4230/lipics.stacs.2019.35 dblp:conf/stacs/HjulerIPS19 fatcat:q4rqsmigcjhuxd4wynla2z7f5m

Connected Dominating Sets [chapter]

Yiwei Wu, Yingshu Li
2012 Ad Hoc and Sensor Wireless Networks: Architectures, Algorithms and Protocols  
Thus, a Connected Dominating Set (CDS) has been recommended to serve as a virtual backbone for a WSN to reduce routing overhead.  ...  After that, we focus on connected dominating set algorithms, including both centralized and distributed, for how to construct CDS. Theoretical analysis are also presented.  ...  A set C ⊂ V is a k-connected m-dominating set (kmCDS) of graph G(V,E)if the induced subgraph G (C, E ) is k-vertex connected and the set C is also an m-dominating set of G.  ... 
doi:10.2174/978160805018510901010019 fatcat:cixydjydrba4bhvfkya3pryz3e

Online Dominating Set

Joan Boyar, Stephan J. Eidenbenz, Lene M. Favrholdt, Michal Kotrbčík, Kim S. Larsen
2018 Algorithmica  
This paper is devoted to the online dominating set problem and its variants.  ...  There is relatively little difference observed between three of the variants of Dominating Set considered: Dominating Set, Connected Dominating Set, and Total Dominating Set.  ...  For Dominating Set, Connected Dominating Set, and Total Dominating Set, we start by using the size of a given dominating set to bound the sizes of some connected or incremental equivalents.  ... 
doi:10.1007/s00453-018-0519-1 fatcat:onlesjjc4vdynnftzfrl6gdgua

Online Dominating Set [article]

Joan Boyar, Stephan J. Eidenbenz, Lene M. Favrholdt, Michal Kotrbčík, Kim S. Larsen
2018 arXiv   pre-print
This paper is devoted to the online dominating set problem and its variants.  ...  There is relatively little difference observed between three of the variants of Dominating Set considered: Dominating Set, Connected Dominating Set, and Total Dominating Set.  ...  For Dominating Set, Connected Dominating Set, and Total Dominating Set, we start by using the size of a given dominating set to bound the sizes of some connected or incremental equivalents.  ... 
arXiv:1604.05172v2 fatcat:6uthyextzndqrbtyxdarsc2cuy

Online Dominating Set and Independent Set [article]

Minati De, Sambhav Khurana, Satyam Singh
2021 arXiv   pre-print
For each of these families, we also present lower bounds of the minimum connected dominating set problem.  ...  We prove that the well known online greedy algorithm for dominating set achieves optimal competitive ratio ζ for any graph.  ...  A dominating set D is said to be an independent dominating set (IDS) if the induced subgraph G[D] is an independent set.  ... 
arXiv:2111.07812v1 fatcat:w75orojoonhdbnuepeg6xdq5qu

Partial vs. Complete Domination: t-Dominating Set [chapter]

Joachim Kneis, Daniel Mölle, Peter Rossmanith
2007 Lecture Notes in Computer Science  
SET can be solved with exponential small error probability in time O((4 + 6α) t · t 6 · n 1 2α +1 ).  ...  Unbalanced case: • Good coloring: 2 −t • Recursive call: 1 2 • Total failure probability: Balanced case: • Good coloring: 2 −t • Recursive call: 1 2 · 1 2 • Total failure probability: Let 0 < α ≤ 1/25. t -DOMINATING  ... 
doi:10.1007/978-3-540-69507-3_31 fatcat:ni3b4oatjvhvrebwkyogfvbgkq

Dominating Sets and Domination Polynomials of Paths

Saeid Alikhani, Yee-Hock Peng
2009 International Journal of Mathematics and Mathematical Sciences  
A setS⊆Vis a dominating set ofG, if every vertex inV\Sis adjacent to at least one vertex inS.  ...  Let&#x1D4AB;nibe the family of all dominating sets of a pathPnwith cardinalityi, and letd(Pn,j)=|&#x1D4AB;nj|. In this paper, we construct&#x1D4AB;ni, and obtain a recursive formula ford(Pn,i).  ...  Corresponding author : alidino.jumani@salu.edu.The domination set D is now union of the Cartesian product of the sets and Lemma 4 : 4 for each G−layer the domination set consists of a single vertex,  ... 
doi:10.1155/2009/542040 fatcat:6xiwohaf5vchdaq4ddeek6vx3q

Dominating sets and Domination polynomials of Cycles [article]

Saeid Alikhani, Yee-hock Peng
2009 arXiv   pre-print
A set S⊂ V is a dominating set of G, if every vertex in V is adjacent to at least one vertex in S.  ...  Let C_n^i be the family of dominating sets of a cycle C_n with cardinality i, and let d(C_n,i) = | C_n^i. In this paper, we construct C_n^i, and obtain a recursive formula for d(C_n, i).  ...  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. The domination number γ(G) is the minimum cardinality of a dominating set in G.  ... 
arXiv:0905.3268v1 fatcat:fp3aloyolra6vkucb65l2kowt4

Reconfiguration of dominating sets

Akira Suzuki, Amer E. Mouawad, Naomi Nishimura
2015 Journal of combinatorial optimization  
We explore a reconfiguration version of the dominating set problem, where a dominating set in a graph G is a set S of vertices such that each vertex is either in S or has a neighbour in S.  ...  Two dominating sets are adjacent if one can be formed from the other by the addition or deletion of a single vertex.  ...  A vertex v in a dominating set S is deletable if S \ {v} is also a dominating set of G.  ... 
doi:10.1007/s10878-015-9947-x fatcat:iq6rjeongnhephjksvdusv3np4

Restricted-sum-dominant sets [article]

Raj Kumar Mistri, R. Thangadurai
2017 arXiv   pre-print
The set A is called a sum-dominant (SD) set if |A + A| > |A - A|, and it is called a restricted sum-domonant (RSD) set if |A A| > |A - A|.  ...  We also provide an explicit construction of infinite sequence of RSD sets.  ...  The restricted-sum-dominant sets of integers have been studied recently by D. Penman and M. Wells [11] .  ... 
arXiv:1712.09226v1 fatcat:gtpmkunahfgvzh4bn34kzvby6m

Enumerating Connected Dominating Sets [article]

Faisal Abu-Khzam, Henning Fernau, Benjamin Gras, Mathieu Liedloff, Kevin Mann
2022 arXiv   pre-print
delay by showing that a polynomial-delay enumeration algorithm for minimal connected dominating sets implies an affirmative algorithmic solution to the Hitting Set Transversal problem.  ...  More precisely, we prove that it is NP-complete to decide, given a graph G and a vertex set U, if there exists a minimal connected dominating set D with U⊆ D, even if G is known to be 2-degenerate.  ...  We can extend set-valued functions to set arguments; for instance, N G [S] = v∈S N G [v] for a set of vertices S; S is a dominating set if N G [S] = V .  ... 
arXiv:2205.00086v1 fatcat:db75f35k2vdlnjthmegktmcst4

Reconfiguration of Dominating Sets [article]

Akira Suzuki, Amer E. Mouawad, Naomi Nishimura
2014 arXiv   pre-print
We explore a reconfiguration version of the dominating set problem, where a dominating set in a graph G is a set S of vertices such that each vertex is either in S or has a neighbour in S.  ...  Two dominating sets are adjacent if one can be formed from the other by the addition or deletion of a single vertex.  ...  A vertex v in a dominating set S is deletable if S \ {v} is also a dominating set of G.  ... 
arXiv:1401.5714v2 fatcat:43cvcehofnak5nkp3td2cjwurq

Reconfiguration of Dominating Sets [chapter]

Akira Suzuki, Amer E. Mouawad, Naomi Nishimura
2014 Lecture Notes in Computer Science  
We explore a reconfiguration version of the dominating set problem, where a dominating set in a graph G is a set S of vertices such that each vertex is either in S or has a neighbour in S.  ...  Two dominating sets are adjacent if one can be formed from the other by the addition or deletion of a single vertex.  ...  A vertex v in a dominating set S is deletable if S \ {v} is also a dominating set of G.  ... 
doi:10.1007/978-3-319-08783-2_35 fatcat:xt5bijpazfc4xhxchombuta7me

Unique Efficient Dominating Sets

Isaac Reiter, Ju Zhou
2020 Open Journal of Discrete Mathematics  
For a graph G, a set D is called a unique efficient dominating set of G if it is the only efficient dominating set of G.  ...  If a dominating set is both independent and perfect, then it is called an efficient dominating set.  ...  Zhou dominates its neighbors and itself when it is in the dominating set. Using this convention, an efficient dominating set is a dominating set that dominates every vertex in a graph exactly once.  ... 
doi:10.4236/ojdm.2020.102006 fatcat:i4maxma4mfdhhdvbqahcrhagz4
« Previous Showing results 1 — 15 out of 4,549,998 results