In this paper, simple optimal algorithms are presented for solving some problems related to interval graphs. These problems are the connected component problem, the spanning tree problem, the eccentricity problem, and...
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In this paper, simple optimal algorithms are presented for solving some problems related to interval graphs. These problems are the connected component problem, the spanning tree problem, the eccentricity problem, and the single source all destinations shortest path problem. All of the above four problems can be solved in linear time if the endpoints of the intervals are sorted. Moreover, our algorithms can be parallelized very easily so that the above problems can be solved in O(log n) time with O(n/log n) processors using the EREW PRAM model.
We present efficient algorithms for the nearest neighbor problem defined in an n × n binary image. We show that using a linear array with a reconfigurable pipelined bus system (LARPBS) of n2processors, the ne...
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We present efficient algorithms for the nearest neighbor problem defined in an n × n binary image. We show that using a linear array with a reconfigurable pipelined bus system (LARPBS) of n2processors, the nearest neighbor problem can be solved in O(loglogn) time, and using an LARPBS of n2+εprocessors, for any fixed constant ε>0. the nearest neighbor problem can be solved in O(l) time. We also show that the nearest neighbor problem can be solved on an LARPBS of n2processors in O(1) time with high probability.
Using a directed acyclic graph (dag) model of algorithms, we solve a problem related to precedence-constrained multiprocessor schedules for array computations: Given a sequence of dags and linear schedules parametrize...
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Using a directed acyclic graph (dag) model of algorithms, we solve a problem related to precedence-constrained multiprocessor schedules for array computations: Given a sequence of dags and linear schedules parametrized by n, compute a lower bound on the number of processors required by the schedule as a function of n. In our formulation, the number of tasks that are scheduled for execution during any fixed time step is the number of non-negative integer solutions dn to a set of parametric linear Diophantine equations. We present an algorithm based on generating functions for constructing a formula for these numbers dn. The algorithm has been implemented as a Mathematica program. Example runs and the symbolic formulas for processor lower bounds automatically produced by the algorithm for Matrix-Vector Product, Triangular Matrix Product, and Gaussian Elimination problems are presented. Our approach actually solves the following more general problem: Given an arbitrary r× s integral matrix A and r-dimensiona...
In this paper we present two advanced methods for evolutionary optimisation. One method is based on parallel Genetic algorithms. It is called Cooperating Populations with Different Evolution Behaviours (CoPDEB), and a...
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In this paper we present two advanced methods for evolutionary optimisation. One method is based on parallel Genetic algorithms. It is called Cooperating Populations with Different Evolution Behaviours (CoPDEB), and allows each population to exhibit a different evolution behaviour. Results from two problems show the advantage of using different evolution behaviour on each population. The other method concerns application of GAs on constrained optimisation problems. It is called the Varying Fitness Function (VFF) method and implements a fitness function with varying penalty tenns, added to the objective function for penalising infeasible solutions, in order to assist the GA to easily locate the area of the global optimum. Simulation results on two real world problems show that the VFF method outperfonns the classic static fitness function implementations.
We present optimal parallel algorithms that run in time on mesh-connected computer for a number of fundamental problems concerning proximity and visibility in a simple polygon. These include computing shortest paths, ...
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We present optimal parallel algorithms that run in time on mesh-connected computer for a number of fundamental problems concerning proximity and visibility in a simple polygon. These include computing shortest paths, shortest path trees, shortest path partitions, all-farthest neighbors, the visibility polygon of a point, the weak visibility polygon of an edge, and the ray shooting problem.
We consider a new supercube architecture, a new interconnection network derived from the hypercube. The supcrcube retains the connectivity and diameter properties of the corresponding hypercube. The embedding of one i...
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We consider a new supercube architecture, a new interconnection network derived from the hypercube. The supcrcube retains the connectivity and diameter properties of the corresponding hypercube. The embedding of one interconnection network into another is a very important issue in the design and analysis of parallel algorithms. In this paper, the problem of embedding and reconfiguring complete binary tree structures is considered in a supercube with faulty nodes. We also propose a new method for embedding and reconfiguring complete binary trees in a faulty supercube. Furthermore, the results enable us to obtain a good method for embedding complete binary tree structures into a faulty supercube with n-expansion. The result enables us to obtain O(n2 - m2) faults which can be tolerated, where (n - 1) is the dimension of a supercube and (m - 1) is the height of a complete binary tree.
Consider the selection problem of determining the k th smallest element of a sequence of n elements. Under the CGM (Coarse Grained Multicomputer) model with p processors and O(n/p) local memory, we present a determini...
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ISBN:
(纸本)9780897919845
Consider the selection problem of determining the k th smallest element of a sequence of n elements. Under the CGM (Coarse Grained Multicomputer) model with p processors and O(n/p) local memory, we present a deterministic parallel algorithm for the selection problem that requires O(log p) communication rounds. Besides requiring a low number of communication rounds, the algorithm also attempts to minimize the total amount of data transmitted in each round (only O(p) except in the last round). The basic algorithm is then extended to solve the problem of q simultaneous selections using the same input sequence, also in O(log p) communication rounds and asymptotically same local computing time (if q = O(p) ). The simultaneous selection algorithm gives rise to a communication efficient sorting algorithm, with O(log p) communication rounds and a total of O(p 2) data transmitted in each round except in the last one. In addition to showing theoretical complexities, we present very promising experimental results obtained on two parallel machines that show almost linear speedup, indicating the efficiency and scalability of the proposed algorithms. To our knowledge, this is the best deterministic CGM algorithm in the literature for the selection problem.
Trapezoid graphs are a superclass of permutation graphs and interval graphs. This paper presents first parallel algorithms for the independent domination, total domination, connected domination and domination problems...
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Trapezoid graphs are a superclass of permutation graphs and interval graphs. This paper presents first parallel algorithms for the independent domination, total domination, connected domination and domination problems in weighted trapezoid graphs. All these algorithms take O(log(2)n) time on a EREW PRAM. The number of processors required is O(max{n(3)/log(2)n,n(2.376)}) for the independent domination problem, and O(max{nm(2)/log(2)n,m(2.376)}) for the other domination problems, where m is the number of edges in a trapezoid graph of n vertices.
The heap representation of priority queues is one of the most widely used data structures in the design of parallel algorithms. Efficiently exploiting the parallelism of a priority heap has significant influence on th...
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