Alan Gibbons

A Optimal Parallel Algorithm for Dynamic Epression Evaluation and its Applications

We describe a deterministic parallel algorithm to compute algebraic expressions in log n time using n/log(n) processors on a parallel random access machine without write conflicts (P-RAM) with no free preprocessing. The input to our algorithm is a string, given by an array, of the expression. Such a form for the input enables a consecutive numbering of the operands in the expression in log(n) time with n/log(n) processors. This corresponds to a consecutive numbering of leaves in the tree of the expression which further enables a suitable partitioning of the leaves into small segments. We improve the result of Miller and Reif (1985), who described an optimal parallel randomized algorithm. Our algorithm can be used to construct optimal parallel algorithms for the recognition of two nontrivial subclasses of context-free languages: bracket and input-driven languages. These languages are the most complicated context-free languages known to be recognizable in deterministic logarithmic space. This strengthens the result of Matheyses and Fiduccia (1982) who constructed an almost optimal parallel algorithm for Dyck languages, since Dyck languages are a proper subclass of input-driven languages.

The MINSUMCUT problem

In this paper we first present a sequential linear algorithm for a linear arrangement problem on trees, MINSUMCUT, and then an O(log n)-time parallel algorithm for MINSUMCUT on trees, which uses n2/(logn) processors.

On the decidability of some problems about rational subsets of free partially commutative monoids

Let I=A+B be a partially commutative alphabet such that two letters commute if one of them belongs to A and the other one belongs to B. Let M=A* B* denote the free partially commutative monoid generated by I. We consider the following six problems for rational (given by regular expressions) subsets X, Y of M: n nQ1:X ∩ Y= O? nQ2: X ⊆ Y? nDI X = Y? nQ4: X = M? nL25: M — X finite? nX is recognizable? n nIt was proved by Choffrut (see [2]) that all these problems are undecidable if Card A > 1 and Card B > 1, and they are decidable if Card A = Card B = 1 (Card U denotes the cardinality of U). It was conjectured (see [2], p 79) that these problems are decidable in the remaining cases, where Card A = 1 and Card B > 1. In this paper we show that if Card A = 1 and Card B > 1 then the problem 01 is decidable, and problems Q2-06 are undecidable. Our paper is an application of results concerning reversal-bounded nondeterministic multicounter machines and nondeterministic general sequential machines.

A class of problems efficiently solvable on mesh-connected computers including dynamic expression evaluation

We show that the problem of dynamic expression evaluation belongs to a class of problems which are efficiently solvable on mesh-connected computers. On efficiently solvable problem is a problem which is solvable in O(r) parallel time using O(n) processors

Dense edge-disjoint embedding of binary trees in the mesh

We present an embedding of the complete binary tree with n leaves in the Vn x Vn mesh, for any n = 2exp(2m) where m is a positive integer. The embedding has the following properties: at most two tree nodes (one of which is a leaf) are mapped onto each mesh node, paths of the tree are mapped onto edge-disjoint paths in the mesh (each mesh edge considered as two anti-parallel directed edges) and the maximum distance from a leaf to the root of the tree is Vn + O (log n) mesh steps. This embedding facilitates efficient implementation of many P-RAM algorithms on the mesh, particularly those using the balanced binary tree technique. Such an embedding offers greater flexibility of use and improves the time complexity of these implementations by a constant factor compared with previously described embeddings.

Collaborative R&D projects: a framework for effective management

There is a growing trend toward collaboration, both between companies and between academia and industry, driven by the knowledge that the sharing of information and technology enhances the generation of innovation. However, collaborations rarely achieve their full potential because of difficulties managing across organisational boundaries. The identification of success factors in collaboration management has therefore been the subject of considerable research. However, the current body of knowledge provides no practical guidance as to how the full range of these success factors could be applied in the everyday context of managing a collaboration, The framework presented here provides a mechanism for achieving effective collaboration management in the form of a simple-to-use management tool.

Parallel algorithms for the minimum cut and the minimum length tree layout problems

Abstract The minimum cut and minimum length linear arrangement problems usually occur in solving wiring problems and have a lot in common with job sequencing questions. Both problems are NP-complete for general graphs and in P for trees. We present here two parallel algorithms for the CREW PRAM. The first solves the minimum length linear arrangement problem for trees and the second solves the minimum cut arrangement for trees. We prove that the first problem belongs to NC for trees, and the second problem is in NC for bounded degree trees. To the best of our knowledge, these are the first parallel algorithms for the minimum length and the minimum cut linear arrangement problems.

The balanced binary tree technique on mesh-connected computers

We show how the balnced binary tree technique can be effectively utilised (to solve problems of size n and implying a balanced binary tree xith n leaves) on a square mesh of n processing elements.

Collaborative R&D projects: a best practice management model

The sharing of information and expertise has been shown to enhance innovation. Therefore, against a background of increasing international competition and rapid technological change, there is an increasing trend toward collaboration between companies, and between universities and industry. However, collaborations are difficult to manage and often fail. Studies of inter-organisational collaborations identified management factors that increase the probability that a collaboration will be successful. Equivalent studies of university-industry collaborations have concentrated on the cultural gap between academia and industry. This research demonstrates that these inter-organisational success factors apply across types of collaboration and across industries, and that their influence extends beyond inter-organisational R&D partnerships to university-industry collaborations. The result of this work is a generic best practice model for the effective management of technological collaborations.

Dense edge-disjoint embedding of complete binary trees in the hypercube

Abstract We show that the complete binary tree with n > 8 leaves can be embedded in the hypercube with n nodes such that: paths of the tree are mapped onto edge-disjoint paths of the hypercube, at most two tree nodes (one of which is a leaf) are mapped onto each hypercube node, and the maximum distance from a leaf to the root of the tree is log2n + 1 hypercube edges (which is optimally short). This embedding facilitates efficient implementation of many P-RAM algorithms on the hypercube.