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Abstract: Based on Huffman tree method, we propose a new 2D graphic representation of protein sequence. This representation can completely avoid loss of information in the transfer of data from a protein sequence to its graphic representation. The method consists of two parts. One is about the 0–1 codes of 20 amino acids by Huffman tree with amino acid frequency. The amino acid frequency is defined as the statistical number of an amino acid in the analyzed protein sequences. The other is about the 2D graphic representation of protein sequence based on the 0–1 codes. Then the applications of the method on ten ND5 genes and seven Escherichia coli strains are presented in detail. The results show that the proposed model may provide us with some new sights to understand the evolution patterns determined from protein sequences and complete genomes. [Copyright &y& Elsevier]

Abstract: Given a search space , an unknown element and fixed integers and , a -ary -restricted query is of the following form: which one of the set is the in?, where is a partition of and for . The problem of finding from with -ary size-restricted queries is called as a -ary search game with small sets. In this paper, we consider sequential algorithms for the above problem, and establish the minimum number of average-case sequential queries when satisfies the uniform distribution on . [Copyright &y& Elsevier]

There were few research works are continuing to increase the performance of Huffman coding. The proposed paper is based on the new technique region based Huffman to increase the performance of the Huffman coding. The proposed technique divides the input file into a number of regions. Huffman codes are obtained for entire file. For each region, the code between the maximum frequency element of that region and maximum frequency element of entire file are interchanged and the symbols of that region are compressed. This is repeated for each region. Then a small variation of the technique is proposed where instead of interchanging the codes of elements, selection of number of region is done by a proposed algorithm. This modified technique eliminates some limitations of previous proposed technique. Comparisons are made among these two variants with classical Huffman technique. [ABSTRACT FROM AUTHOR]

Abstract: The following restricted model of coin-weighing problem is considered: there is a heavier coin in a set of n coins, of which are good coins having the same weight. The test device is a two-arms balance scale and each test-set is of the form with , where is a given integer. We present an optimal sequential algorithm requiring the minimal average cost of weighings when the probability distribution on the coin set is uniform distribution. [Copyright &y& Elsevier]

Abstract: In the partial alphabetic tree problem we are given a multiset of non-negative weights , partitioned into blocks . We want to find a binary tree T where the elements of W reside in its leaves such that if we traverse the leaves from left to right then all leaves of precede all leaves of for every . Furthermore among all such trees, T has to minimize , where is the depth of in T. The partial alphabetic tree problem generalizes the problem of finding a Huffman tree over W (there is only one block) and the problem of finding a minimum cost alphabetic tree over W (each block consists of a single item). This problem arises when we need an optimal binary code for a set of items with known frequencies, such that we have a lexicographic restriction for some of the codewords. Our main result is a pseudo-polynomial time algorithm that finds the optimal tree. Our algorithm runs in time where , , and ( is the golden ratio). In particular the running time is polynomial in case the weights are bounded by a polynomial of n. To bound the running time of our algorithm we prove an upper bound of on the depth of the optimal tree. Our algorithm relies on a solution to what we call the layered Huffman forest problem which is of independent interest. In the layered Huffman forest problem we are given an unordered multiset of weights , and a multiset of integers . We look for a forest F with k trees, , where the weights in W correspond to the leaves of F, that minimizes where is the depth of in its tree plus if . Our algorithm for this problem runs in time. [Copyright &y& Elsevier]