Given a positive integer @math , a @math -dominating set in a graph @math is a set of vertices such that every vertex not in the set has at least @math neighbors in the set. A total @math -dominating set, also known as a @math -tuple total dominating set, is a set of vertices such that every vertex of the graph has at least @math neighbors in the set. The problems of finding the minimum size of a @math -dominating, resp. total @math -dominating set, in a given graph, are referred to as @math -domination, resp. total @math -domination. These generalizations of the classical domination and total domination problems are known to be NP-hard in the class of chordal graphs, and, more specifically, even in the classes of split graphs (both problems) and undirected path graphs (in the case of total @math -domination). On the other hand, it follows from recent work by (2017) that these two families of problems are solvable in time @math in the class of interval graphs. In this work, we develop faster algorithms for @math -domination and total @math -domination in the class of proper interval graphs. The algorithms run in time @math for each fixed @math and are also applicable to the weighted case.
We now give an overview of related work and compare our results with the most related other results, in addition to those due to @cite_60 , which motivated this work.
@cite_60
2017562693 2122778642 2029099433 2107972503
In the past several years studies have started to appear comparing the accuracies of various science mapping approaches. These studies primarily compare the cluster solutions resulting from different similarity approaches, and give varying results. In this study we compare the accuracies of cluster solutions of a large corpus of 2,153,769 recent articles from the biomedical literature (2004–2008) using four similarity approaches: co-citation analysis, bibliographic coupling, direct citation, and a bibliographic coupling-based citation-text hybrid approach. Each of the four approaches can be considered a way to represent the research front in biomedicine, and each is able to successfully cluster over 92p of the corpus. Accuracies are compared using two metrics—within-cluster textual coherence as defined by the Jensen-Shannon divergence, and a concentration measure based on the grant-to-article linkages indexed in MEDLINE. Of the three pure citation-based approaches, bibliographic coupling slightly outperforms co-citation analysis using both accuracy measures; direct citation is the least accurate mapping approach by far. The hybrid approach improves upon the bibliographic coupling results in all respects. We consider the results of this study to be robust given the very large size of the corpus, and the specificity of the accuracy measures used. © 2010 Wiley Periodicals, Inc. When we write or prepare to write a research paper, we always have appropriate references in mind. However, there are most likely references we have missed and should have been read and cited. As such a good citation recommendation system would not only improve our paper but, overall, the efficiency and quality of literature search. Usually, a citation's context contains explicit words explaining the citation. Using this, we propose a method that "translates" research papers into references. By considering the citations and their contexts from existing papers as parallel data written in two different "languages", we adopt the translation model to create a relationship between these two "vocabularies". Experiments on both CiteSeer and CiteULike dataset show that our approach outperforms other baseline methods and increase the precision, recall and f-measure by at least 5 to 10 , respectively. In addition, our approach runs much faster in the both training and recommending stage, which proves the effectiveness and the scalability of our work. Citation relationship between scientific publications has been successfully used for scholarly bibliometrics, information retrieval and data mining tasks, and citation-based recommendation algorithms are well documented. While previous studies investigated citation relations from various viewpoints, most of them share the same assumption that, if paper1 cites paper2 (or author1 cites author2), they are connected, regardless of citation importance, sentiment, reason, topic, or motivation. However, this assumption is oversimplified. In this study, we employ an innovative "context-rich heterogeneous network" approach, which paves a new way for citation recommendation task. In the network, we characterize 1) the importance of citation relationships between citing and cited papers, and 2) the topical citation motivation. Unlike earlier studies, the citation information, in this paper, is characterized by citation textual contexts extracted from the full-text citing paper. We also propose algorithm to cope with the situation when large portion of full-text missing information exists in the bibliographic repository. Evaluation results show that, context-rich heterogeneous network can significantly enhance the citation recommendation performance. The old Asian legend about the blind men and the elephant comes to mind when looking at how different authors of scientific papers describe a piece of related prior work. It turns out that different citations to the same paper often focus on different aspects of that paper and that neither provides a full description of its full set of contributions. In this article, we will describe our investigation of this phenomenon. We studied citation summaries in the context of research papers in the biomedical domain. A citation summary is the set of citing sentences for a given article and can be used as a surrogate for the actual article in a variety of scenarios. It contains information that was deemed by peers to be important. Our study shows that citation summaries overlap to some extent with the abstracts of the papers and that they also differ from them in that they focus on different aspects of these papers than do the abstracts. In addition to this, co-cited articles (which are pairs of articles cited by another article) tend to be similar. We show results based on a lexical similarity metric called cohesion to justify our claims. © 2008 Wiley Periodicals, Inc.