Left-weight sequences (LW-sequences for short) are in common currency for encoding binary trees. In [16], Wu et al. proposed an algorithm associated with tree rotations for listing all binary trees in diverse representations including LW-sequences. In particular, such a list of LW-sequences is generated in Gray-code order. In this paper, based on this ordering, we present efficient ranking and unranking algorithms. For binary trees with n internal nodes, the time complexity and the space requirement in each of our ranking and unranking algorithms are O(n2) and O(n), respectively.

A non-regular tree T with a prescribed branching sequence (s1,s2,...,sn) is a rooted and ordered tree such that its internal nodes are numbered from 1 to n in preorder and every internal node i in T has si children. Recently, Wu et al. (2010) introduced a concise representation called RD-sequences to represent all non-regular trees and proposed a loopless algorithm for generating all non-regular trees in a Gray-code order. In this paper, based on such a Gray-code order, we present efficient ranking and unranking algorithms of non-regular trees with n internal nodes. Moreover, we show that the ranking algorithm and the unranking algorithm can be run in O(n2) time and O(n2+nSn-1) time, respectively, provided a preprocessing takes O(n2Sn-1) time and space in advance, where .

Social bookmarking services have recently made it possible for us to register and share our own bookmarks on the web and are attracting attention. The services let us get structured data: (URL, Username, Timestamp, Tag Set). And these data represent user interest in web pages. The number of bookmarks is a barometer of web page value. Some web pages have many bookmarks, but most of those bookmarks may have been posted far in the past. Therefore, even if a web page has many bookmarks, their value is not guaranteed. If most of the bookmarks are very old, the page may be obsolete. In this paper, by focusing on the timestamp sequence of social bookmarkings on web pages, we model their activation levels representing current values. Further, we improve our previously proposed ranking method for web search by introducing the activation level concept. Finally, through experiments, we show effectiveness of the proposed ranking method.