New Parallel Sorting Schemes

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / DAAB-07-72-C-0259National Science Foundation / NSF MCS-76-1732

Computing the Yolk in Spatial Voting Games without Computing Median Lines

The yolk is an important concept in spatial voting games as it generalises the equilibrium and provides bounds on the uncovered set. We present near-linear time algorithms for computing the yolk in the spatial voting model in the plane. To the best of our knowledge our algorithm is the first algorithm that does not require precomputing the median lines and hence able to break the existing $O(n^{4/3})$ bound which equals the known upper bound on the number of median lines. We avoid this requirement by using Megiddo's parametric search, which is a powerful framework that could lead to faster algorithms for many other spatial voting problems

Coverability in 1-VASS with Disequality Tests

We study a class of reachability problems in weighted graphs with constraints on the accumulated weight of paths. The problems we study can equivalently be formulated in the model of vector addition systems with states (VASS). We consider a version of the vertex-to-vertex reachability problem in which the accumulated weight of a path is required always to be non-negative. This is equivalent to the so-called control-state reachability problem (also called the coverability problem) for 1-dimensional VASS. We show that this problem lies in NC: the class of problems solvable in polylogarithmic parallel time. In our main result we generalise the problem to allow disequality constraints on edges (i.e., we allow edges to be disabled if the accumulated weight is equal to a specific value). We show that in this case the vertex-to-vertex reachability problem is solvable in polynomial time even though a shortest path may have exponential length. In the language of VASS this means that control-state reachability is in polynomial time for 1-dimensional VASS with disequality tests

The VLSI Optimality of the AKS Sorting Network

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / N00014-79-C-0424IBM Predoctoral Fellowship Progra

A taxonomy of parallel sorting

TR 84-601In this paper, we propose a taxonomy of parallel sorting that includes a broad range of array and file sorting algorithms. We analyze the evolution of research on parallel sorting, from the earliest sorting networks to the shared memory algorithms and the VLSI sorters. In the context of sorting networks, we describe two fundamental parallel merging schemes - the odd-even and the bitonic merge. Sorting algorithms have been derived from these merging algorithms for parallel computers where processors communicate through interconnection networks such as the perfect shuffle, the mesh and a number of other sparse networks. After describing the network sorting algorithms, we show that, with a shared memory model of parallel computation, faster algorithms have been derived from parallel enumeration sorting schemes, where keys are first ranked and then rearranged according to their rank

A Minimum Area VLSI Architecture for O(logn) Time Sorting

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / N00014-79-C-0424IBM predoctoral Fellowshi

Parallel Algorithms for the Maximum Flow

The problem of finding the maximal flow through a given network has been intensively studied over the years. The classic algorithm for this problem given by Ford and Fulkerson has been developed and improved by a number of authors including Edmonds and Karp. With the advent of parallel computers, it is of great interest to see whether more efficient algorithms can be designed and implemented. The networks which we will consider will be both capacitated and bounded. Compared with a capacitated network, the problem of finding a flow through a bounded network is much more complicated in that a transformation into an auxiliary network is required before a feasible flow can be found. In this thesis, we review the algorithms of Ford and Fulkerson and Edmonds and Karp and implement them in a standard sequential way. We also implement the transformation required to handle the case of a bounded network. We then develop two parallel algorithms, the first being a parallel version of the Edmonds and Karp algorithm while the second applies the Breadth-First search technique to extract as much parallelism as possible from the problem. Both these algorithms have been written in the Occam programming language and implemented on a transputer system consisting of an IBM PC host, a B004 single transputer board and a network of four transputers contained on a B003 board supplied by Inmos Ltd. This is an example of a multiprocessor machine with independent memory. The relative efficiency of the algorithms has been studied and we present tables of the execution times taken over a variety of test networks. The transformation of the original network into an auxiliary network has also been implemented using parallel techniques and the problems encountered in the development of the algorithm are described. We have also investigated in detail one of the few parallel algorithms for this problem described in the literature due to Shiloach and Vishkin. This algorithm is described in the thesis. It has not been possible to implement this algorithm because it is specifically designed to run on a multiprocessor machine with shared memory