An incremental version of the k-center problem on boundary of a convex polygon

Du, Haibo; Xu, Yinfeng; Zhu, Binhai

doi:10.1007/s10878-015-9933-3

Cited by 6 publications

(3 citation statements)

References 27 publications

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“…Motivated by location problems,

p

‐centres in graphs have been the subject of much research. This study was focussed almost exclusively on algorithms to find a

p

‐centre of a graph (see, eg, ). The quantitative aspect of

p

‐centres, that is, how far at most a vertex can be from a

p

‐centre of a graph, which is expressed by the

p

‐radius, has received hardly any attention in the literature, except for the special case

p = 1

, which is the classical radius.…”

Section: Bounds On the Bold-italicp‐radiusmentioning

confidence: 99%

Distance domination and generalized eccentricity in graphs with given minimum degree

Dankelmann

Erwin

2019

Journal of Graph Theory

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Let G be a connected graph and k∈double-struckN. The k‐distance domination number of G is the smallest cardinality of a set S of vertices such that every vertex of G is within distance k from some vertex of S. While for k=1, that is, for the ordinary domination number, the problem of finding asymptotically sharp upper bounds in terms of order and minimum degree of the graph has been solved, corresponding bounds for k>1 have remained elusive. In this paper, we solve this problem and present an asymptotically sharp upper bound on the k‐distance domination number of a graph in terms of its order and minimum degree, which significantly improves on bounds in the literature. We also obtain an asymptotically sharp upper bound on the p‐radius of graphs in terms of order and minimum degree. For p∈double-struckN, the p‐radius of G is defined as the smallest integer d such that there exists a set S of p vertices of G having the property that every vertex of G is within distance d of some vertex in S. We also present improved bounds for graphs of given order, minimum degree and maximum degree, for triangle‐free graphs and for graphs not containing a 4‐cycle as a subgraph.

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“…Motivated by location problems,

p

‐centres in graphs have been the subject of much research. This study was focussed almost exclusively on algorithms to find a

p

‐centre of a graph (see, eg, ). The quantitative aspect of

p

‐centres, that is, how far at most a vertex can be from a

p

‐centre of a graph, which is expressed by the

p

‐radius, has received hardly any attention in the literature, except for the special case

p = 1

, which is the classical radius.…”

Section: Bounds On the Bold-italicp‐radiusmentioning

confidence: 99%

Distance domination and generalized eccentricity in graphs with given minimum degree

Dankelmann

Erwin

2019

Journal of Graph Theory

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“…For example, some special constraints on the centers positions were added to the problem. In 2015, Du et al [30] explored the incremental one that all the centers should lie on the boundary of a convex polygon. In the same year, Liang et al [31] addressed the constraint of vertexes with internal connectedness, where it is guaranteed that any two nodes in one set should be lined by an internal path.…”

Section: The -Center Problemmentioning

confidence: 99%

An Energy Balancing Strategy Based on Hilbert Curve and Genetic Algorithm for Wireless Sensor Networks

Kong

Pan

Sung

et al. 2017

Wireless Communications and Mobile Computing

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A wireless sensor network is a sensing system composed of a few or thousands of sensor nodes. These nodes, however, are powered by internal batteries, which cannot be recharged or replaced, and have a limited lifespan. Traditional two-tier networks with one sink node are thus vulnerable to communication gaps caused by nodes dying when their battery power is depleted. In such cases, some nodes are disconnected with the sink node because intermediary nodes on the transmission path are dead. Energy load balancing is a technique for extending the lifespan of node batteries, thus preventing communication gaps and extending the network lifespan. However, while energy conservation is important, strategies that make the best use of available energy are also important. To decrease transmission energy cost and prolong network lifespan, a three-tier wireless sensor network is proposed, in which the first level is the sink node and the third-level nodes communicate with the sink node via the service sites on the second level. Moreover, this study aims to minimize the number of service sites to decrease the construction cost. Statistical evaluation criteria are used as benchmarks to compare traditional methods and the proposed method in the simulations.

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“…In [20] a detailed overview of the various methods and algorithms used to solve this problem is given. They are mainly used for problems related to locating different types of objects [21]- [26].…”

Section: Introductionmentioning

confidence: 99%

An analysis between exact and approximate algorithms for the k-center problem in graphs

Kralev

Kraleva

Ankov

et al. 2022

IJECE

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<span lang="EN-US">This research focuses on the k-center problem and its applications. Different methods for solving this problem are analyzed. The implementations of an exact algorithm and of an approximate algorithm are presented. The source code and the computation complexity of these algorithms are presented and analyzed. The multitasking mode of the operating system is taken into account considering the execution time of the algorithms. The results show that the approximate algorithm finds solutions that are not worse than two times optimal. In some case these solutions are very close to the optimal solutions, but this is true only for graphs with a smaller number of nodes. As the number of nodes in the graph increases (respectively the number of edges increases), the approximate solutions deviate from the optimal ones, but remain acceptable. These results give reason to conclude that for graphs with a small number of nodes the approximate algorithm finds comparable solutions with those founds by the exact algorithm.</span>

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An incremental version of the k-center problem on boundary of a convex polygon

Cited by 6 publications

References 27 publications

Distance domination and generalized eccentricity in graphs with given minimum degree

Distance domination and generalized eccentricity in graphs with given minimum degree

An Energy Balancing Strategy Based on Hilbert Curve and Genetic Algorithm for Wireless Sensor Networks

An analysis between exact and approximate algorithms for the k-center problem in graphs

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