The time required to compute any function of a collection of circular doubly linked lists on a CROW PRAM is shown to be at most a constant factor more than on a CREW PRAM, but this is not true for singly linked lists....
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ISBN:
(纸本)0897913701
The time required to compute any function of a collection of circular doubly linked lists on a CROW PRAM is shown to be at most a constant factor more than on a CREW PRAM, but this is not true for singly linked lists. A tight lower bound of Ω(log log n) for colouring an n node doubly linked list on a CROW PRAM using a constant number of colours is also obtained.
A unified framework for finding efficient permutation routes on parallel networks in an off-line setting is presented. If the underlying graph of a parallel network contains an appropriate 'approximate' produc...
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ISBN:
(纸本)0897913701
A unified framework for finding efficient permutation routes on parallel networks in an off-line setting is presented. If the underlying graph of a parallel network contains an appropriate 'approximate' product structure then our method guarantees the existence of non-blocking near-optimal permutation routes. The routes in question can be determined in polynomial time. Furthermore, our results are extended to finding permutation routes among the remaining 'live' nodes in a faulty network.
We introduce a task scheduling model which is useful in the design and analysis of algorithms for small parallel machines. We prove that under our model, the overhead experienced in scheduling an n × n grid graph...
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ISBN:
(纸本)0897913701
We introduce a task scheduling model which is useful in the design and analysis of algorithms for small parallel machines. We prove that under our model, the overhead experienced in scheduling an n × n grid graph is O(log log n) for p processors, p ≥ 2. We also prove a matching lower bound of Ω(log log n) for p processors, p ≥ 2. We give an extension of the model to cover the case where the processors can have varying speed or are subject to delay.
The Program Dependence Graph (PDG), which represents the data and the control dependences of a program is considered. Attention is limited to the subgraph of the PDG which contains only the control dependence edges. T...
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ISBN:
(纸本)0897913701
The Program Dependence Graph (PDG), which represents the data and the control dependences of a program is considered. Attention is limited to the subgraph of the PDG which contains only the control dependence edges. This subgraph is called the Control Dependence Graph (CDG). The authors formalize what it means for a CDG to have a corresponding sequential version and characterize the conditions under which there is such a corresponding sequentialization not requiring duplication.
The problem of representing a set U = {u1, ..., um} of read-write variables on an n-node distributed memory parallel computer is considered. It is shown that U can be represented among the n nodes of a variant of the ...
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ISBN:
(纸本)0897913701
The problem of representing a set U = {u1, ..., um} of read-write variables on an n-node distributed memory parallel computer is considered. It is shown that U can be represented among the n nodes of a variant of the mesh-of-trees using O((m/n)polylog(m/n)) storage per node such that any n-tuple of variables may be accessed in O(log n(log log n)2) time in the worst case for m polynomial in n.
This paper investigates the parallel time and processor complexities of several searching problems involving Monge and Monge-composite arrays. We present array-searching algorithms for concurrent-read-concurrent-write...
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ISBN:
(纸本)0897913701
This paper investigates the parallel time and processor complexities of several searching problems involving Monge and Monge-composite arrays. We present array-searching algorithms for concurrent-read-concurrent-write (CRCW) PRAMs, concurrent-read-exclusive-write (CREW) PRAMs, hypercubes, cube-connected-cycles, and shuffle-exchange networks. All these algorithms run in optimal time, and their processor-time products are all within an O(lg n) factor of the worst-case sequential bounds. Several applications of these algorithms are also given. Two applications improve previous results substantially, and the others provide novel parallelalgorithms for problems not previously considered.
In this paper we consider the problem of generating random permutations on small parallel machines. The machines that we have in mind are shared memory machines with a constant number of processors such as the Sequent...
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ISBN:
(纸本)0897913701
In this paper we consider the problem of generating random permutations on small parallel machines. The machines that we have in mind are shared memory machines with a constant number of processors such as the Sequent Symmetry. We describe a parallel implementation of the 'shuffling' algorithm for generating a random permutation. If the hardware operates in a fair manner, this algorithm generates a fully random permutation. However, if the machine resolves contention in a malicious manner, then the algorithm does not generate permutations uniformly. We give almost tight bounds on the degree that an adversary can reduce the randomness. We also discuss the cost of locking data in the algorithm and present a method of generating random permutations with substantially reduced locking cost.
We present a parallel randomized algorithm for finding if two planar graphs are isomorphic. Assuming that we have a tree of separators for each planar graph, our algorithm takes O(log(n)) time with P = (n1.5&middo...
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ISBN:
(纸本)0897913701
We present a parallel randomized algorithm for finding if two planar graphs are isomorphic. Assuming that we have a tree of separators for each planar graph, our algorithm takes O(log(n)) time with P = (n1.5·√log(n)) processors with probability to fail of 1/n or less, where n is the number of vertices. The algorithms needs 2·log(m)·log(n) + O(log(n)) random bits. The number of random bits can be decreased to O(log(n)) by increasing the processors number to n3/2+Ε. This algorithm significantly improves the previous results of n4 processors.
The authors address the apparently difficult problem of doing parallel transitive closure when the (directed) graph is sparse and/or, only single-source information is desired. O(e) work is their target for the single...
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ISBN:
(纸本)0897913701
The authors address the apparently difficult problem of doing parallel transitive closure when the (directed) graph is sparse and/or, only single-source information is desired. O(e) work is their target for the single-source problem. When the graph is sparse, then the all-pairs transitive closure problem can be solved by performing a depth-first search from each node, taking O(ne) time;that is their target for the all-pairs problem. The authors do not reach either target, except for the all-pairs case when e is fairly large. However, they make significant progress, in the sense that they have the first algorithms that simultaneously use time much less than linear and use work that is less than M(n).
Space-efficient Information Dispersal Algorithm (IDA) [11] is applied to parallel communication in the hypercube. Let N denote the size of the network. Our communication scheme runs in 2·log N + 1 time using cons...
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ISBN:
(纸本)0897913701
Space-efficient Information Dispersal Algorithm (IDA) [11] is applied to parallel communication in the hypercube. Let N denote the size of the network. Our communication scheme runs in 2·log N + 1 time using constant size buffers. Its probability of successful routing is at least 1 - N-2.419·log N+1.5, proving Rabin's conjecture. The same scheme also tolerates O(N) random link failures with high probability. The scheme runs within the said time bound without long delay. On-line and efficient wire testing and replacement on the hypercube can be realized if our fault-tolerant routing scheme is used. Let α denote the total number of links in the hypercube. It is shown that ≈ α/352 wires can be disabled simultaneously without disrupting the ongoing computation or degrading the routing performance much.
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