Tree Languages Defined in First-Order Logic with One Quantifier Alternation

We study tree languages that can be defined in \Delta_2 . These are tree languages definable by a first-order formula whose quantifier prefix is forall exists, and simultaneously by a first-order formula whose quantifier prefix is . For the quantifier free part we consider two signatures, either the descendant relation alone or together with the lexicographical order relation on nodes. We provide an effective characterization of tree and forest languages definable in \Delta_2 . This characterization is in terms of algebraic equations. Over words, the class of word languages definable in \Delta_2 forms a robust class, which was given an effective algebraic characterization by Pin and Weil

CloudTree: A Library to Extend Cloud Services for Trees

In this work, we propose a library that enables on a cloud the creation and management of tree data structures from a cloud client. As a proof of concept, we implement a new cloud service CloudTree. With CloudTree, users are able to organize big data into tree data structures of their choice that are physically stored in a cloud. We use caching, prefetching, and aggregation techniques in the design and implementation of CloudTree to enhance performance. We have implemented the services of Binary Search Trees (BST) and Prefix Trees as current members in CloudTree and have benchmarked their performance using the Amazon Cloud. The idea and techniques in the design and implementation of a BST and prefix tree is generic and thus can also be used for other types of trees such as B-tree, and other link-based data structures such as linked lists and graphs. Preliminary experimental results show that CloudTree is useful and efficient for various big data applications

Optimal Prefix Codes with Fewer Distinct Codeword Lengths are Faster to Construct

A new method for constructing minimum-redundancy binary prefix codes is described. Our method does not explicitly build a Huffman tree; instead it uses a property of optimal prefix codes to compute the codeword lengths corresponding to the input weights. Let $n$ be the number of weights and $k$ be the number of distinct codeword lengths as produced by the algorithm for the optimum codes. The running time of our algorithm is $O(k \cdot n)$. Following our previous work in \cite{be}, no algorithm can possibly construct optimal prefix codes in $o(k \cdot n)$ time. When the given weights are presorted our algorithm performs $O(9^k \cdot \log^{2k}{n})$ comparisons.Comment: 23 pages, a preliminary version appeared in STACS 200

Algorithms for High-Speed Routing in IP Networks

Práce se zabývá simulací algoritmů vyhledávajících v IP sítích nejdelší shodný prefix, konkrétně Trie, Tree Bitmap a Shape Shifting Trie. Algoritmy jsou implementovány softwarově a je zkoumána jejich paměťová a výpočetní náročnost.This work deals with simulation of algorithms finding the longest matching prefix in IP networks, particularly Trie, Tree Bitmap and Shape Shifting Trie. Algorithms are software implemented and explored about their memory and computational performance.

APPLYING THE ATTRIBUTED PREFIX TREE FOR MINING CLOSED SEQUENTIAL PATTERNS

Mining closed sequential patterns is one of important tasks in data mining. It is proposed to resolve difficult problems in mining sequential pattern such as mining long frequent sequences that contain a combinatorial number of frequent subsequences or using very low support thresholds to mine sequential patterns is usually both time- and memory-consuming. This paper applies the characteristics of closed sequential patterns and sequence extensions into the prefix tree structure to mine closed sequential patterns from the sequence database. The paper uses the parent–child relationship on prefix tree structure and each node on prefix tree is also added fields to determine whether that is a closed sequential pattern or not. Experimental results show that the number of sequential patterns is reduced significantly