Dominating sets in directed graphs

Pang, Chaoyi; Zhang, Rui; Zhang, Qing; Wang, Junhu

doi:10.1016/j.ins.2010.06.009

Cited by 44 publications

(16 citation statements)

References 7 publications

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“…This can be expected to be technically more demanding than the solutions to the corresponding problems on undirected graphs. A natural starting point would be the consideration of domination-type problems in directed graphs, not only because this type of problem (on undirected graphs) was one of the main driving forces behind the development of Measure&Conquer, but also because there has been quite some recent interest in the database community on this type of problems on directed graphs, as can be seen in [21] and the literature quoted therein. The most common definition of a dominating set D in a directed graph G = (V , A) seems to be to require that for each vertex w / ∈ D, there is some v ∈ D such that (v, w) ∈ A; see [15].…”

Section: Discussionmentioning

confidence: 99%

An exact exponential-time algorithm for the Directed Maximum Leaf Spanning Tree problem

Binkele-Raible

Fernau

2012

Journal of Discrete Algorithms

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NP-hard problems on directed graphs Outbranching with a maximum number of leaves Given a directed graph G = (V , A), the Directed Maximum Leaf Spanning Tree problem asks to compute a directed spanning tree with as many leaves as possible. By designing a branching algorithm analyzed with Measure&Conquer, we show that the problem can be solved in time O * (1.9044 n ) using polynomial space. Allowing exponential space, this run time upper bound can be lowered to O * (1.8139 n ). We also provide an example showing a lower-bound for the running time of our algorithm.

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Section: Discussionmentioning

confidence: 99%

An exact exponential-time algorithm for the Directed Maximum Leaf Spanning Tree problem

Binkele-Raible

Fernau

2012

Journal of Discrete Algorithms

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“…In order to obtain our main results, we need the following definition of domination in graphs [16,17]. Let = ( ( ), ( )) be a directed graph.…”

Section: Preliminariesmentioning

confidence: 99%

Fixed Point Theorems for Multivalued NonselfG-Almost Contractions in Banach Spaces Endowed with Graphs

Tiammee

Charoensawan

Suantai

2017

Journal of Function Spaces

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“…In Milner and Woodrow [1989] a number of conditions for the existence of an independent dominating set for a number of different kinds of graphs are provided. Some related work also exists on locating minimum dominating (but not independent) sets (e.g., Pang et al [2010] and Chartrand et al [1999]). …”

Section: Related Workmentioning

confidence: 99%

Multiple Radii DisC Diversity

Δρόσου

Pitoura

2015

ACM Trans. Database Syst.

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Recently, result diversification has attracted a lot of attention as a means to improve the quality of results retrieved by user queries. In this article, we introduce a novel definition of diversity called DisC diversity. Given a tuning parameter r, which we call radius, we consider two items to be similar if their distance is smaller than or equal to r. A DisC diverse subset of a result contains items such that each item in the result is represented by a similar item in the diverse subset and the items in the diverse subset are dissimilar to each other. We show that locating a minimum DisC diverse subset is an NP-hard problem and provide algorithms for its approximation. We extend our definition to the multiple radii case, where each item is associated with a different radius based on its importance, relevance, or other factors. We also propose adapting DisC diverse subsets to a different degree of diversification by adjusting r, that is, increasing the radius (or zooming-out) and decreasing the radius (or zooming-in). We present efficient implementations of our algorithms based on the M-tree, a spatial index structure, and experimentally evaluate their performance.

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Dominating sets in directed graphs

Cited by 44 publications

References 7 publications

An exact exponential-time algorithm for the Directed Maximum Leaf Spanning Tree problem

An exact exponential-time algorithm for the Directed Maximum Leaf Spanning Tree problem

Fixed Point Theorems for Multivalued NonselfG-Almost Contractions in Banach Spaces Endowed with Graphs

Multiple Radii DisC Diversity

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