Aaron M. Tenenbaum

Two Spectra of Self-Organizing Sequential Search Algorithms

Two sets of algorithms for searching and dynamic reorganization of linear lists are presented. Each set forms a spectrum, with the well-known move-to-front and transposition algorithms at the extrema. A linear ordering on the stationary expected search cost of the algorithms in each of the two spectra is established over a restricted set of probability distributions.

Simulations of dynamic sequential search algorithms

In [3], R.L. Rivest presents a set of methods for dynamically reordering a sequential list containing <italic>N</italic> records in order to increase search efficiency. The method <italic>A<subscrpt>i</subscrpt></italic> (for <italic>i</italic> between 1 and <italic>N</italic>) performs the following operation each time that a record <italic>R</italic> has been successfully retrieved: Move <italic>R</italic> forward <italic>i</italic> positions in the list, or to the front of the list if it was in a position less than <italic>i</italic>. The method <italic>A</italic><subscrpt>1</subscrpt> is called the transposition method, and the method <italic>A</italic><subscrpt><italic>N</italic>-1</subscrpt> is called the move-to-front method.

An empirical comparison of B-trees, compact B-trees and multiway trees

It is well-known that the B-tree data structure yields excellent worst-case search costs and for that reason is widely employed in the organization of external files and in the implementation of data bases. In this paper, we examine general B-trees empirically and compare them with a less restrictive structure, the general multiway tree, and a more restrictive structure, the compact B-tree. We compare search costs, insertion costs, and space costs of these three structures for both small and large orders and indicate their relative utility for large and small data sets. Although there are cases when general multiway trees are more effective than B-trees, this is not the case for most practical situations. Compact B-trees are also shown to degrade rapidly in the presence of insertions and are therefore only useful for static data sets.

Compile time type determination in SETL

In this paper, some features of the SETL language are presented. Also discussed are two methods for determining the data types of runtime objects in higher level languages from the static program text. The first method determines the type of a variable from the way in which it is defined, while the second method determines its type from the way it is subsequently used. This technique is shown to be of value in producing optimized object code. An implementation of the technique is also discussed and an example of the results produced under the implementation for a specific SETL program is presented.

Program efficiency and data structures

Program efficiency is usually considered from the point of view of optimizing code. Selecting a proper data structure can have a remarkable effect on the efficiency of the final program. In this paper it is shown how one problem can be solved in several ways using several different data structures. The efficiency of the programs depend on the data structures selected.

P-trees: storage efficient multiway trees

A new variation of high order multiway tree structures, the P-tree is presented. P-trees have average access costs that are significantly better than those of B-trees and are no worse (and often better) in storage utilization. Unlike compact B-trees, they can be maintained dynamically, and unlike dense multiway trees and B-trees, their associated insertion algorithm, which is also presented, is cheap and involves (at most) a very localized rearrangement of keys.

A lesson in recursion and structured programming

Students in middle level courses in data structures and programming languages often do not have a full appreciation of recursion. The study of the simulation of recursion can be an excellent tool in improving this situation. It is shown how to construct a nonrecursive routine to solve a problem whose solution is naturally recursive. This nonrecursive routine is then used as a foundation from which one can construct a simpler and better structured program than the original version. The advantages of this activity are also discussed.

Memory utilization efficiency under a class of first-fit algorithms

This paper examines an improved version of a modified first-fit storage allocation algorithm. In this version, small blocks of free storage are not permitted to remain on the free list but instead are placed on a separate sliver list, available for recombination with newly freed blocks. The memory utilization efficiency of a system under this algorithm is shown to be markedly superior to a system using an algorithm in which such blocks are unavailable for either allocation or recombination.

Monetary values: double trouble or dollars and sense?

It is curious but there is widespread misuse of floating-point types to represent monetary amounts in introductory programming classes. This is evident from a survey of popular CS1 textbooks. It is instructive to examine how dollars and cents and other currency values are represented in actual practice and how we can utilize those techniques in computer science education, for both the sake of correctness and to illustrate important general principles. Furthermore, it is particularly interesting to review the history of CS education and determine how this situation came to pass. The interplay between technology, academic cultures and institutional development turns out to be quite significant.

A system for labor negotiations

The paper describes a computer system to determine salary costs in a work force which contains different salary levels and in which employees are being promoted to higher levels. The system is based on a mathematical model of employee promotional behavior which is described in the paper. The system was used in recent contract negotiations to estimate labor costs for proposed contracts. Experience with the system is described and further extentions of the system are proposed.