Discrete tomography deals with the reconstruction of discrete sets with given projections relative to a limited number of directions, modeling the situation where a material is studied through x-rays and we desire to reconstruct an image representing the scanned object. In many cases it would be interesting to consider the projections to be related to more than one distinguishable type of cell, called atoms or colors, as in the case of a scan involving materials of different densities, as a bone and a muscle. Unfortunately the general n-color problem with n > 1 is NP-complete, but in this paper we show how several polynomial reconstruction algorithms can be defined by assuming some prior knowledge on the set to be rebuilt. In detail, we study the cases where the union of the colors form a set without switches, a convex polyomino or a convex 8-connected set. We describe some efficient reconstruction algorithms and in a case we give a sufficient condition for uniqueness.

When planning a database, the problem of index selection is of particular interest. The authors examine a transaction model that includes queries, updates, insertions, and deletions, and they define a function that calculates the transaction's total cost when an index set is used. Their aim is to minimize the function cost in order to identify the optimal set. The algorithms proposed in other studies require an exponential time in the number of attributes in order to solve the problem. The authors propose a heuristic algorithm based on some properties of the cost function that produces an almost optimal set in polynomial time. In many cases, the cost function properties make it possible to prove that the solution obtained is the optimal one.>

Abstract In this paper a system for software development is described. This system consists of a general‐purpose macroprocessor and a set of service programs. The macroprocessor has been planned to work in a conversational environment and to this purpose a set of utilities has been inserted to aid the editing and the debugging of the macrodefinitions. Indeed the system allows the user to select, by means of commands, the flow of the operations to be executed and to choose when and how any program has to be expanded. The macroprocessor is easy to use and it is suitable to generate codes for both high‐level languages and assembler languages.