对哈夫曼树唯一性的探讨

在我们的日常教学中,我们经常会对哈夫曼树的建立给出不同答案,那么是否有唯一标准答案?通过相关程序流程及代码实验,分析了导致认为创建哈夫曼树不唯一的原因,说明了在一种既定的算法下,我们是可以达到哈夫曼树建立的唯一性的.     

哈夫曼算法的改进与应用

哈夫曼树是带权路径长度(WPL)最小的二叉树,通过对哈夫曼算法的研究,提出一种求取哈夫曼树带权路径长度的改进方法,简化运算,有效提高求取WPL的效率和正确性。同时利用哈夫曼算法进行数据压缩,获得明显的压缩效果。     

哈夫曼算法的改进与应用

哈夫曼树是带权路径长度（WPL）最小的二叉树，通过对哈夫曼算法的研究，提出一种求取哈夫曼树带权路径长度的改进方法，简化运算．有效提高求取WPL的效率和正确性。同时利用哈夫曼算法进行数据压缩，获得明显的压缩效果。     

A fast algorithm for Huffman decoding based on a recursion Huffman tree

This paper focuses on the time efficiency of Huffman decoding. In this paper, we utilize numerical interpretation to speed up the decoding process. The proposed algorithm firstly transforms the given Huffman tree into a recursion Huffman tree. Then, with the help of the recursion Huffman tree, the algorithm has the possibility to decode more than one symbol at a time if the minimum code length is less than or equal to half of the width of the processing unit. When the minimum code length is larger than the half of the width of the processing unit, the proposed method can still increase the average symbols decoded in one table access (thus speeding up the decoding time). In fact, the experimental results of the test files show that the average number of decoded symbols at one time for the proposed method ranges from 1.91 to 2.13 when the processing unit is 10. The experimental comparisons show that, compared to the conventional binary tree search method and the level-compressed Huffman decoding method, the decoding time of the proposed method is a great improvement.     

一种不用建造Huffman树的高效Huffman编码算法

Huffman编码作为一种高效的不等长编码技术正日益广泛地在文本、图像、视频压缩及通信、密码等领域得到应用。为了更有效地利用内存空间、简化编码步骤和相关操作,首先研究了重建Huffman树所需要的信息,并提出通过对一类一维结构数组进行相关操作来获取上述信息的方法,然后利用这些信息,并依据提出的规范Huffman树的编码性质,便能直接得到Huffman编码。与传统的Huffman算法及近年来国内外文献中提出的改进算法相比,由于该方法不需要构造Huffman树,不仅使内存需求大大减少,而且编码步骤和相关操作更简洁,因而更利于程序的实现和移植。更重要的是,该算法思路为Huffman算法的研究和发展提供了新的途径。     

构造赫夫曼树的高效算法

构造特定的赫夫曼树是编译码的前提,为此提出了一种新的赫夫曼树构造算法,以提高赫夫曼树的构造效率。     

Huffman-based join-exit-tree scheme for contributory key management

Time efficiency in key establishment and rekeying is one of the major problems contributory key management schemes strive to address. Some schemes have been put forward to improve time efficiencies of key establishment and key update, yet they did not consider the scenario where users have varying costs and capabilities. Although conference key tree based on Huffman coding has been proposed to obtain minimum average cost on key establishment considering users' differences, it did not give the efficient key updating algorithm. We propose a Huffman-based join-exit-tree (HJET) scheme to minimizing the average key establishment time and reducing the key rekeying time for join/departure events. HJET scheme separates users into subgroups according to users' locations, designs the key tree of each subgroup using Huffman coding, and lets the combined weights locate in a higher place of the Huffman tree to minimize the key establishment time. To reduce the key rekeying cost, join tree and exit tree are adopted and served as the temporary buffers for joining and leaving users. Performance analysis and simulation results demonstrate that HJET is efficient in key establishment and update, and achieves the asymptotic time cost of O(1) for join event and nearly O(1)for leave events when group dynamics are known a priori.     

Huffman算法的改进及其在图像压缩中的应用

本文改进了Huffman编码算法,主要是针对Huffman编码生成Huffman树构造中的排序方法的改进,提出一种基于"堆排序"的新方法。采用堆排序找到最小值实现Huffman编码,经过这种改进的Huffman编码方法对内存读写的次数大为减少,从而提高了响应速度。使得Huffman编码效率有所提高。通过对JPEG的Huffman压缩算法的分析以及采用4个JPG文件对改进的和传统的Huffman算法进行了仿真实验,对比分析表明改进算法的性能无论是压缩比率还是压缩时间方面都比经典的Huffman算法性能有所提高。     

Restricted ground tree transducers

We consider restricted versions of ground tree transducers: total, deterministic, and symmetric subclasses and all other subclasses created by applying any combination of these restrictions. We present the inclusion diagram of the tree transformation classes induced by these restricted ground tree transducers. We show that the following four classes of term relations are the same: (i) tree transformations induced by symmetric deterministic ground tree transducers, (ii) congruence relations on term algebras induced by reduced ground term rewriting systems, (iii) congruence relations on term algebras induced by convergent ground term rewriting systems, and (iv) finitely generated congruence relations on term algebras. As a by-product of our results, we obtain a new ground completion algorithm. Moreover, we show that the following three classes of term relations on term algebras with at least one non-nullary function symbol are also the same: (i) tree transformations induced by total symmetric deterministic ground tree transducers, (ii) congruence relations on term algebras of finite index, (iii) finitely generated congruence relations on term algebras of which the trunk is the whole set of terms.     

哈夫曼树在多重判定程序中的运用

本文首先介绍了哈夫曼算法及多重判定结构程序设计原理,并以教务管理系统为例讨论了在多重判定程序设计中,如何运用哈夫曼算法优化程序设计.实例运行结果表明,利用哈夫曼算法可以写出优质的多重判定程序,提高程序的执行效率.     

赫夫曼树遍历算法的优化

对数据结构中赫夫曼树和赫夫曼遍历的算法问题进行探讨,针对传统使用的遍历算法存在循环次数较多、算法时间复杂度较大问题,通过修改参数和循环体结构对原有算法进行改进,从而减少循环次数,降低算法时间复杂度,同时也提出了动态编码算法等的优点和可行性。     

赫夫曼树遍历算法的优化

对数据结构中赫夫曼树和赫夫曼遍历的算法问题进行探讨,针对传统使用的遍历算法存在循环次数较多、算法时间复杂度较大问题,通过修改参数和循环体结构对原有算法进行改进,从而减少循环次数,降低算法时间复杂度,同时也提出了动态编码算法等的优点和可行性。     

On the Huffman and Alphabetic Tree Problem with General Cost Functions

We address generalized versions of the Huffman and Alphabetic Tree Problem where the cost caused by each individual leaf i, instead of being linear, depends on its depth in the tree by an arbitrary function. The objective is to minimize either the total cost or the maximum cost among all leaves. We review and extend the known results in this direction and devise a number of new algorithms and hardness proofs. It turns out that the Dynamic Programming approach for the Alphabetic Tree Problem can be extended to arbitrary cost functions, resulting in a time O(n ⁴) optimal algorithm using space O(n ³). We identify classes of cost functions where the well-known trick to reduce the runtime by a factor of n via a “monotonicity” property can be applied. For the generalized Huffman Tree Problem we show that even the k-ary version can be solved by a generalized version of the Coin Collector Algorithm of Larmore and Hirschberg (in Proc. SODA’90, pp. 310–318, 1990) when the cost functions are nondecreasing and convex. Furthermore, we give an O(n ²logn) algorithm for the worst case minimization variants of both the Huffman and Alphabetic Tree Problem with nondecreasing cost functions. Investigating the limits of computational tractability, we show that the Huffman Tree Problem in its full generality is inapproximable unless P = NP, no matter if the objective function is the sum of leaf costs or their maximum. The alphabetic version becomes NP-hard when the leaf costs are interdependent.     

金融业务数据库的数据压缩方法

针对金融业务中实时数据库的数据存储特点,提出结构混合压缩(SMC)算法。SMC算法利用金融数据具有纯文本、数据分散和数据项内重复少的特点,以哈夫曼编码作为算法基础,根据词频将单字和词组混合,在哈夫曼树中引入数组结构,对文本数据进行压缩。测试结果表明,SMC算法的平均数据压缩率比原始哈夫曼算法提高了约13%。     

哈夫曼树的实现及其在文件压缩中的应用

在信息快速传输和存储的过程中,数据压缩有着非常重要的作用.介绍了基于哈夫曼树的文本压缩和解压缩的原理与方法,并给出了Huiffman压缩与解压程序核心算法的实现过程.     

Huffman算法程序的形式化推导

使用PAR方法形式化推导了解决最优编码问题的Huffman算法。推导过程充分利用最优编码树的特性,在对原问题进行分划归约为子问题时,引入一个新元素来取代原来的2个或多个元素,使用一套接近数学语言的抽象记号表示集合、二叉树等,推导过程简洁且能生成正确的算法。该Huffman算法能在PAR平台上通过自动生成系统转换成可执行语言程序,并正常运行。     

同频率分组的自适应哈夫曼数据压缩算法

在讨论静态和自适应哈夫曼数据压缩算法的优点和不足后,借助于引进两个参数和一个节点符号频数表,提出了按相同频率进行分组的自适应哈夫曼数据压缩算法,减少哈夫曼树的层数。通过对高尔夫球场草坪温湿度的监测,实验表明该算法的压缩比比自适应哈夫曼算法有明显改善,这种算法编码简单、编码速度较快,适合用在能量有限的无线传感器网络的传感器节点。     

安全的LZW编码算法及其在GIF图像加密中的应用

提出了一种安全的LZW编码算法——SLZW。该算法在改进的LZW编码过程中嵌入加密,从而能够同时完成压缩和加密。SLZW编码利用动态Huffman树作为LZW的字典,并且通过耦合映像格子(CML)产生的密钥流对字典的构建和更新进行控制,编码输出进一步和密钥流进行异或后产生密文。并且,该算法被应用于GIF图像加密中,实验结果和分析表明,该算法不仅具有较好的安全性,同时也将标准LZW算法的压缩效率提高了10%左右,具有广泛的实用性。     

哈夫曼树教学探讨

探讨了哈夫曼树的教学要点及教学方法,以哈夫曼树的定义和意义为教学内容的开端,分步介绍了哈夫曼树的构造和运用方法,以典型的电文传输为例,剖析了哈夫曼树的要点以及编码过程的注意点。     

改进的四进制哈夫曼算法

提出了一种改进的四进制哈夫曼树的生成算法,通过分析算法的平均码长和编码效率,论证了算法相对于传统的四进制算法的优点。并用C语言分别实现两种算法,进行了压缩比和压缩时间的比较,证明了改进算法在压缩比和压缩速度上的提升。