440 research outputs found
Source Coding for Quasiarithmetic Penalties
Huffman coding finds a prefix code that minimizes mean codeword length for a
given probability distribution over a finite number of items. Campbell
generalized the Huffman problem to a family of problems in which the goal is to
minimize not mean codeword length but rather a generalized mean known as a
quasiarithmetic or quasilinear mean. Such generalized means have a number of
diverse applications, including applications in queueing. Several
quasiarithmetic-mean problems have novel simple redundancy bounds in terms of a
generalized entropy. A related property involves the existence of optimal
codes: For ``well-behaved'' cost functions, optimal codes always exist for
(possibly infinite-alphabet) sources having finite generalized entropy. Solving
finite instances of such problems is done by generalizing an algorithm for
finding length-limited binary codes to a new algorithm for finding optimal
binary codes for any quasiarithmetic mean with a convex cost function. This
algorithm can be performed using quadratic time and linear space, and can be
extended to other penalty functions, some of which are solvable with similar
space and time complexity, and others of which are solvable with slightly
greater complexity. This reduces the computational complexity of a problem
involving minimum delay in a queue, allows combinations of previously
considered problems to be optimized, and greatly expands the space of problems
solvable in quadratic time and linear space. The algorithm can be extended for
purposes such as breaking ties among possibly different optimal codes, as with
bottom-merge Huffman coding.Comment: 22 pages, 3 figures, submitted to IEEE Trans. Inform. Theory, revised
per suggestions of reader
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 (2)logn) 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.ArticleALGORITHMICA. 69(3): 582-604 (2014)journal articl
Generalizations of Length Limited Huffman Coding for Hierarchical Memory Settings
In this paper, we study the problem of designing prefix-free encoding schemes having minimum average code length that can be decoded efficiently under a decode cost model that captures memory hierarchy induced cost functions. We also study a special case of this problem that is closely related to the length limited Huffman coding (LLHC) problem; we call this the soft-length limited Huffman coding problem. In this version, there is a penalty associated with each of the n characters of the alphabet whose encodings exceed a specified bound D(? n) where the penalty increases linearly with the length of the encoding beyond D. The goal of the problem is to find a prefix-free encoding having minimum average code length and total penalty within a pre-specified bound P. This generalizes the LLHC problem. We present an algorithm to solve this problem that runs in time O(nD). We study a further generalization in which the penalty function and the objective function can both be arbitrary monotonically non-decreasing functions of the codeword length. We provide dynamic programming based exact and PTAS algorithms for this setting
Study of Two Competing Index Mechanisms: Prefix B+-tree and Trie Structures
This thesis deals with two competing index mechanisms, namely, prefix B+-trees and trie structures, which are useful for handling varying size keys in document retrieval systems. Refinements and variants of these two indexing methods are studied. Tradeoffs of storage requirements and retrieval time or performance benefits and maintainance difficulties for various refining approaches are examined.Computing and Information Scienc
IMPROVED LICENSE PLATE LOCALIZATION ALGORITHM BASED ON MORPHOLOGICAL OPERATIONS
Automatic License Plate Recognition (ALPR) systems have become an important tool to track stolen cars, access control, and monitor traffic. ALPR system consists of locating the license plate in an image, followed by character detection and recognition. Since the license plate can exist anywhere within an image, localization is the most important part of ALPR and requires greater processing time. Most ALPR systems are computationally intensive and require a high-performance computer. The proposed algorithm differs significantly from those utilized in previous ALPR technologies by offering a fast algorithm, composed of structural elements which more precisely conducts morphological operations within an image, and can be implemented in portable devices with low computation capabilities. The proposed algorithm is able to accurately detect and differentiate license plates in complex images. This method was first tested through MATLAB with an on-line public database of Greek license plates which is a popular benchmark used in previous works. The proposed algorithm was 100% accurate in all clear images, and achieved 98.45% accuracy when using the entire database which included complex backgrounds and license plates obscured by shadow and dirt. Second, the efficiency of the algorithm was tested in devices with low computational processing power, by translating the code to Python, and was 300% faster than previous work
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