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In Social network system, existing “people you might know” or “Mutual friends” recommending applications are commonly utilized to list two-hop mediate relationships that one could have with another in order to tighten the bonds among groups. However, as the number of SNS users increase dramatically, the relationship data get so huge that the performance of Mutual Friends recommendation system becomes an urgent problem considering the developers’ requirements. Here we propose a sorting algorithm in Hadoop----a parallel computing framework, to enhance the efficiency of “Mutual friends” recommendation process by taking advantage of the novel map reduce model. In the revised application, original sorting algorithm of intermediate data, merge sort, is replaced by a more time saving sorting approach which introduces a B-Tree like data structure, 2-3 Tree to store the user friendship data and conducts the sorting process. As number of user increases, the revised user defined map reduce functions perform better than the conventional design in time consuming aspect.

A tree is scattered if it does not contain a subdivision of the complete binary tree as a subtree. We show that every scattered tree contains a vertex, an edge, or a set of at most two ends preserved by every embedding of T. This extends results of Halin, Polat and Sabidussi. Calling two trees equimorphic if each embeds in the other, we then prove that either every tree that is equimorphic to a scattered tree T is isomorphic to T, or there are infinitely many pairwise non-isomorphic trees which are equimorphic to T. This proves the tree alternative conjecture of Bonato and Tardif for scattered trees, and a conjecture of Tyomkyn for locally finite scattered trees.

This paper presents a method for estimating the cost of tree edit operations. The approach poses the problem as that of estimating a generative model for a set of tree samples. The generative model uses the tree-union as the structural archetype for every tree in the distribution and assigns to each node in the archetype the probability that the node is present in a sample. A minimum descriptor length formulation is then used to estimate the structure and parameters of this tree model as well as the node-correspondences between trees in the sample-set and the tree model.

Several papers describe linear time algorithms to preprocess a tree, such that one can answer subsequent nearest common ancestor queries in constant time. Here, we survey these algorithms and related results. A common idea used by all the algorithms for the problem is that a solution for complete binary trees is straightforward. Furthermore, for complete binary trees we can easily solve the problem in a distributed way by labeling the nodes of the tree such that from the labels of two nodes alone one can compute the label of their nearest common ancestor. Whether it is possible to distribute the data structure into short labels associated with the nodes is important for several applications such as routing. Therefore, related labeling problems have received a lot of attention recently.Previous optimal algorithms for nearest common ancestor queries work using some mapping from a general tree to a complete binary tree. However, it is not clear how to distribute the data structures obtained using these mappings. We conclude our survey with a new simple algorithm that labels the nodes of a rooted tree such that from the labels of two nodes alone one can compute in constant time the label of their nearest common ancestor. The labels assigned by our algorithm are of size $O(\log n)$ bits where $n$ is the number of nodes in the tree. The algorithm runs in $O(n)$ time.

Background This paper is devoted to distance measures for leaf-labelled trees on free leafset. A leaf-labelled tree is a data structure which is a special type of a tree where only leaves (terminal) nodes are labelled. This data structure is used in bioinformatics for modelling of evolution history of genes and species and also in linguistics for modelling of languages evolution history. Many domain specific problems occur and need to be solved with help of tree postprocessing techniques such as distance measures. Results Here we introduce the tree edit distance designed for leaf labelled trees on free leafset, which occurs to be a metric. It is presented together with tree edit consensus tree notion. We provide statistical evaluation of provided measure with respect to R-F, MAST and frequent subsplit based dissimilarity measures as the reference measures. Conclusions The tree edit distance was proven to be a metric and has the advantage of using different costs for contraction and pruning, therefore their properties can be tuned depending on the needs of the user. Two of the presented methods carry the most interesting properties. E(3,1) is very discriminative (having a wide range of values) and has a very regular distance distribution which is similar to a normal distribution in its shape and is good both for similar and non-similar trees. NFC(2,1) on the other hand is proportional or nearly proportional to the number of mutation operations used, irrespective of their type.

A priority queue is a data structure for maintaining a collection of items, each having an associated key, such that the item with the largest key is easily accessible. Priority queues are implemented by using heap, k-ary tree, single linked-list, leftist tree, linked tree, AVL-tree, 2-3 tree, and fixed priority property. Required storage for each method was obtained and the worst case time analysis was done in terms of the number of key comparison and key exchanges during the insertion and deletion process. Finally, each of these methods were run on PIP-11 UNIX TIME SEARING SYSTEM at NPS using different random number generators to get the average CPU times for insertion and deletion process. http://archive.org/details/comparisonndnaly1094517544 Lieutenant, Junior Grade, Turkish Navy Approved for public release; distribution is unlimited.