Eljas Soisalon-Soininen

On the definition and computation of rectilinear convex hulls

Abstract Recently the computation of the rectilinear convex hull of a collection of rectilinear polygons has been studied by a number of authors. From these studies three distinct definitions of rectilinear convex hulls have emerged. We examine these three definitions for point sets in general, pointing out some of their consequences, and we give optimal algorithms to compute the corresponding rectilinear convex hulls of a finite set of points in the plane.

Uncoupling updating and rebalancing in chromatic binary search trees

In order to gain maximal efficiency of the concurrent use of search trees the number of nodes to be locked at a time should be as small aa possible, and the locks should be released aa soon aa possible. We propose a new rebalancing method for binary search treea that allows rebalancing to be uncoupled from updating, so as to make updating faster. The trees we use are obtained by relaxing the balance conditions of red-black trees. When not involved with updating, the rebalancing task can be performed as a shadow process being active all the time, or it can be performed outside rush hours, at night, for example.

The Complexity and Decidability of Separation

We study the difficulty of solving instances of a new family of sliding block puzzles called SEPARATIONTM. Each puzzle in the family consists of an arrangement in the plane of n rectilinear wooden blocks, n > 0. The aim is to discover a sequence of rectilinear moves which when carried out will separate each piece to infinity. If there is such a sequence of moves we say the puzzle or arrangement is separable and if each piece is moved only once we say it is one-separable. Furthermore if it is one-separable with all moves being in the same direction we say it is iso-separable.

Optimal algorithms to compute the closure of a set of iso-rectangles☆

Abstract Three varieties of the closure of a set of iso-(oriented) rectangles, i.e., rectilin-early-oriented rectangles, are introduced. These are uni-directional, diagonal, and rectangular closure. First a strong decomposition theorem for diagonal closure in terms of uni-directional closure is proved. Then time and space optimal algorithms to compute uni-directional and diagonal closure, each running in O ( n log n ) time and O ( n ) space, are described. An O ( n log n ) time and space algorithm for rectangular closure is also described. The algorithm for diagonal closure has applications in database concurrency control: an O ( n log n ) time and O ( n ) space algorithm for testing for safety and detecting deadlocks in locked transaction systems is obtained.

A method for transforming grammars into LL(k) form

SummaryA new method for transforming grammars into equivalent LL(k) grammars is studied. The applicability of the transformation is characterized by defining a subclass of LR(k) grammars, called predictive LR(k) grammars, with the property that a grammar is predictive LR(k) if and only if the corresponding transformed grammar is LL(k). Furthermore, it is shown that deterministic bottom-up parsing of a predictive LR(k) grammar can be done by the LL(k) parser of the transformed grammar. This parsing method is possible since the transformed grammar always ‘left-to-right covers’ the original grammar. The class of predictive LR(k) grammars strictly includes the class of LC(k) grammars (the grammars that can be parsed deterministically in the left-corner manner). Thus our transformation is more powerful than the one previously available, which transforms LC(k) grammars into LL(k) form.

Efficient evaluation for a subset of recursive queries

Well-known results on graph traversal are used to develop a practical, efficient algorithm for evaluating regularly and linearly recursive queries in databases that contain only binary relations. Transformations are given that reduce a subset of regular and linear queries involving n-ary relations (n > 2) to queries involving only binary relations.

Inessential Error Entries and Their Use in LR Parser Optimization

The use of default reductions in implementing LR parsers is considered in conjunction with the desire to decrease the number of states of the parser by making use of dont-care (also called inessential ) error entries. Default reductions are those which are performed independently of the lookahead string when other operations do not apply, and their use can lead to substantial savings in space and time. Dont-care error entries of an LR parser are those which are never consulted, and thus they can be arbitrarily replaced by nonerror entries in order to make a state compatible with another one. Determining dont-care error entries is most important in avoiding the growth of the size of the parser when eliminating reductions by single productions, that is, productions for which the right-hand side is a single symbol. The use of default reductions diminishes dont-care error entries. This effect is analyzed by giving a necessary and sufficient condition for an error entry to be dont-care when default reductions are used. As an application, elimination of reductions by single productions in conjunction with the use of default reductions is considered.

A generalized transitive closure for relational queries

We augment relational algebra with a generalized transitive closure operator that allows for the efficient evaluation of a subclass of recursive queries. The operator is based on a composition operator which is as general as possible when the operator is required to be associative and when only relational algebra operators are used in its definition. The closure of such a composition can be computed using the well-known efficient algorithms designed for the computation of the usual transitive closure. Besides the case in which complete materialization of recursive relations are required, our strategy also yields an efficient solution in the case in which a selection is applied to the closure.

An optimal algorithm for testing for safety and detecting deadlocks in locked transaction systems

Various notions are introduced for the closure of a set of rectilinearly oriented rectangles on the plane. Optimal algorithms are presented for computing the closures. These algorithms imply optimal solutions to several problems related to database concurrency control.

On the covering problem for left-recursive grammars

Abstract Two new proofs of the fact that proper left-recursive grammars can be covered by non-left-recursive grammars are presented. The first proof is based on a simple trick inspired by the over ten-year-old idea that semantic information hanged on the productions can be carried along in the transformations. The second proof involves a new method for eliminating left recursion from a proper context-free grammar in such a way that the covering grammar is obtained directly.