You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Multimedia uploaded content is tagged and recommended by users of collaborative systems, resulting in informal classifications also known as folksonomies. Faceted web ranking has been proved a reasonable alternative to a single ranking which does not take into account a personalized context. In this paper we analyze the online computation of rankings of users associated to facets made up of multiple tags. Possible applications are user reputation evaluation (ego-ranking) and improvement of content quality in case of retrieval. We propose a solution based on PageRank as centrality measure: (i) a ranking for each tag is computed offline on the basis of the corresponding tag-dependent subgraph; (ii) a faceted order is generated by merging rankings corresponding to all the tags in the facet. The fundamental assumption, validated by empirical observations, is that step (i) is scalable. We also present algorithms for part (ii) having time complexity O(k), where k is the number of tags in the facet, well suited to online computation.

Cited Abstract(s):
[1]: The PageRank algorithm, used in the Google search engine, greatly improves the results of Web search by taking into account the link structure of the Web. PageRank assigns to a page a score proportional to the number of times a random surfer would visit that page, if it surfed indefinitely from page to page, following all outlinks from a page with equal probability. We propose to improve PageRank by using a more intelligent surfer, one that is guided by a probabilistic model of the relevance of a page to a query. Efficient execution of our algorithm at query time is made possible by precomputing at crawl time (and thus once for all queries) the necessary terms. Experiments on two large subsets of the Web indicate that our algorithm significantly outperforms PageRank in the (human-rated) quality of the pages returned, while remaining efficient enough to be used in today's large search engines.
Query-dependent PageRank calculation was introduced in Richarson and Domingos [1] to extract a weighted probability per keyword for each webpage. These probabilities are summed up to generate a query-dependent result. They also show that this faceted ranking has, for thousands of keywords, computation and storage requirements that are only approximately @math - @math times greater than that of a single query-independent PageRank. As we show in , our facet-dependent ranking algorithms have similar time complexity.