. H i r s c h b e r g P r i n c e t o n U n i v e r s i t yThe problem of finding a longest common subsequence of two strings has been solved in quadratic time and space. An algorithm is presented which will solve this problem in quadratic time and in linear space.

AaS~ACT Two algorithms are presented that solve the longest common subsequence problem The first algorithm is applicable in the general case and requires O(pn + n log n) time where p is the length of the longest common subsequence The second algorithm requires time bounded by O(p(m + 1 -p)log n) In the common speoal case where p is close to m, this algorithm takes much less time than n ~ KEY WORDS AND PHRASES' subsequence, common subsequence, algorithm CR CATEOORIES 3 73, 3 79, 5 25, 5 39

This paper surveys a variety of data compression methods spanning almost 40 years of research, from the work of Shannon, Fano, and Huffman in the late 1940s to a technique developed in 1986. The aim of data compression is to reduce redundancy in stored or communicated data, thus increasing effective data density. Data compression has important application in the areas of file storage and distributed systems. Concepts from information theory as they relate to the goals and evaluation of data compression methods are discussed briefly. A framework for evaluation and comparison of methods is constructed and applied to the algorithms presented. Comparisons of both theoretical and empirical natures are reported, and possibilities for future research are suggested.

Algorithms that modify the order of linear search lists are surveyed. First the problem, including assumptions and restrictions, is defined. Next a summary of analysis techniques and measurements that apply to these algorithms is given. The main portion of the survey presents algorithms in the literature with absolute analyses when available. The following section gives relative measures that are applied between two or more algorithms. The final section presents open questions.A linear search list is a list of initially unordered records that will be sequentially searched through on the basis of a key value associated with each record. The goal of the search may be merely to see whether the record exists in the list, to look up data associated with the key, or to modify data within the record. A linear search list is ordered in the sense that searches may only progress linearly (from the first record until the desired record is found or the end of the list is encountered). The list is generally implemented as a sequentially allocated array (either containing the records or pointers to them) or as a linked list. Linear searches on such a list are required in cases in which the list is linked or the elements are not ordered in any way that would facilitate faster search techniques.It is assumed that some records are accessed more frequently than others. A selforganizing linear search list may permute the order of the records in some fashion after a record is found, attempting to place the more frequently accessed records closer to the front of the list to reduce future search times. What algorithms can be used for this permutation and how they perform relative to each other in terms of expected search time are the questions that we address in this article.Two examples of simple permutation algorithms are moue-to-front, which moves the accessed record to the front of the list, shifting all records previously ahead of it back one position, and transpose, which