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Efficient Parallel Algorithms for Tree Accumulations
 Science of Computer Programming
, 1994
"... Accumulations are higherorder operations on structured objects; they leave the shape of an object unchanged, but replace elements of that object with accumulated information about other elements. Upwards and downwards accumulations on trees are two such operations; they form the basis of many tree ..."
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Accumulations are higherorder operations on structured objects; they leave the shape of an object unchanged, but replace elements of that object with accumulated information about other elements. Upwards and downwards accumulations on trees are two such operations; they form the basis of many tree algorithms. We present two Erew Pram algorithms for computing accumulations on trees taking O(log n) time on O(n= log n) processors, which is optimal.
Dynamic parallel tree contraction
 In Proceedings 5th Annual ACM Symp. on Parallel Algorithms and Architectures
, 1994
"... Parallel tree contraction has been found to be a useful and quite powerful tool for the design of a wide class of efficient graph algorithms. We propose a corresponding technique for the parallel solution of problems with incremental changes in the data. In dynamic tree contraction problems, we are ..."
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Parallel tree contraction has been found to be a useful and quite powerful tool for the design of a wide class of efficient graph algorithms. We propose a corresponding technique for the parallel solution of problems with incremental changes in the data. In dynamic tree contraction problems, we are given an initial tree T, and then an online algorithm processes requests regarding T. Requests may be either incremental changes to T or requests for certain values computed using the tree. A simple example is maintaining the preorder numbering on a tree. The online algorithm would then have to handle incremental changes to the tree, and would also have to quickly answer queries about the preorder number of any tree node. Our dynamic algorithms are based on the prior parallel tree contraction algorithms, and hence we call such algorithms incremental tree contraction algorithms. By maintaining the connection between our incremental algorithms and the parallel tree contraction algorithm, we create incremental algorithms for tree contraction. We consider a dynamic binary tree T of ≤ n nodes and unbounded depth. We describe a procedure, which we call the dynamic parallel tree contraction algorithm, which incrementally processes various parallel modification requests and queries: (1) parallel requests to add or delete leaves of T, or modify labels of internal nodes or leaves of T, and also (2) parallel tree contraction queries which require recomputing values at specified nodes. Each modification or query is with respect to a set of nodes U in T. We make use of a random splitting tree as an aid
The Owner Concept for PRAMs
, 1991
"... We analyze the owner concept for PRAMs. In OROWPRAMs each memory cell has one distinct processor that is the only one allowed to write into this memory cell and one distinct processor that is the only one allowed to read from it. By symmetric pointer doubling, a new proof technique for OROWPRAMs, ..."
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Cited by 19 (5 self)
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We analyze the owner concept for PRAMs. In OROWPRAMs each memory cell has one distinct processor that is the only one allowed to write into this memory cell and one distinct processor that is the only one allowed to read from it. By symmetric pointer doubling, a new proof technique for OROWPRAMs, it is shown that list ranking can be done in O(log n) time by an OROWPRAM and that LOGSPACE ` OROWTIME(log n). Then we prove that OROWPRAMs are a fairly robust model and recognize the same class of languages when the model is modified in several ways and that all kinds of PRAMs intertwine with the NC hierarchy without timeloss. Finally it is shown that EREWPRAMs can be simulated by OREWPRAMs and ERCWPRAMs by ORCWPRAMs. 3 This research was partially supported by the Deutsche Forschungsgemeinschaft, SFB 342, Teilprojekt A4 "Klassifikation und Parallelisierung durch Reduktionsanalyse" y Email: rossmani@lan.informatik.tumuenchen.dbp.de Introduction Fortune and Wyllie introduced in...
Parallel Implementation of Tree Skeletons
 Journal of Parallel and Distributed Computing
, 1996
"... Trees are a useful data type, but they are not routinely included in parallel programming systems because their irregular structure makes them seem hard to compute with e ciently. Wepresent a method for constructing implementations of skeletons, highlevel homomorphic operations on trees, that execu ..."
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Trees are a useful data type, but they are not routinely included in parallel programming systems because their irregular structure makes them seem hard to compute with e ciently. Wepresent a method for constructing implementations of skeletons, highlevel homomorphic operations on trees, that execute in parallel. In particular, we consider the case where the size of the tree is much larger than the the number of processors available, so that tree data must be partitioned. The approach uses the theory of categorical data types to derive implementation templates based on tree contraction. Many useful tree operations can be computed in time logarithmic in the size of their argument, on a wide range of parallel systems. 1 Contribution One common approach to generalpurpose parallel computation is based on packaging complex operations as templates, or skeletons [3, 12]. Skeletons encapsulate the control and data ow necessary to compute useful operations. This permits software to be written in a way that is independent of particular architectures, and indeed of underlying parallelism at all, while freeing implementations
Linear Time Algorithm to Recognize Clustered Planar Graphs and its Parallelization
 98, 3rd Latin American symposium on theoretical informatics
, 1998
"... We develop a linear time algorithm for the following problem: Given a graph G and a hierarchical clustering of the vertices, such that all clusters induce connected subgraphs, determine whether G can be embedded into the plane, such that no cluster has a hole. This is an improvement to the O(n 2 )a ..."
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We develop a linear time algorithm for the following problem: Given a graph G and a hierarchical clustering of the vertices, such that all clusters induce connected subgraphs, determine whether G can be embedded into the plane, such that no cluster has a hole. This is an improvement to the O(n 2 )algorithm of Q.W. Feng et al. [6] and the algorithm of Lengauer [12].
Extended Fibonacci cubes
 IEEE Trans. Parallel Distr. Systems
, 1997
"... Abstract—The Fibonacci Cube is an interconnection network that possesses many desirable properties that are important in network design and application. The Fibonacci Cube can efficiently emulate many hypercube algorithms and uses fewer links than the comparable hypercube, while its size does not in ..."
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Abstract—The Fibonacci Cube is an interconnection network that possesses many desirable properties that are important in network design and application. The Fibonacci Cube can efficiently emulate many hypercube algorithms and uses fewer links than the comparable hypercube, while its size does not increase as fast as the hypercube. However, most Fibonacci Cubes (more than 2/3 of all) are not Hamiltonian. In this paper, we propose an Extended Fibonacci Cube (EFC 1) with an even number of nodes. It is defined based on the same sequence F(i) = F(i 1) + F(i 2) as the regular Fibonacci sequence; however, its initial conditions are different. We show that the Extended Fibonacci Cube includes the Fibonacci Cube as a subgraph and maintains its sparsity property. In addition, it is Hamiltonian and is better in emulating other topologies. Specifically, the Extended Fibonacci Cube can embed binary trees more efficiently than the regular Fibonacci Cube and is almost as efficient as the hypercube, even though the Extended Fibonacci Cube is a much sparser network than the hypercube. We also propose a series of Extended Fibonacci Cubes with even number of nodes. Any Extended Fibonacci Cube (EFC k, with k ≥ 1) in the series contains the node set of any other cube that precedes EFC k in the series. We show that any Extended Fibonacci Cube maintains virtually all the desirable properties of the Fibonacci Cube. The EFC k s can be considered as flexible versions of incomplete hypercubes, which eliminates their restriction on the number of nodes, and, thus, makes it possible to construct parallel machines with arbitrary sizes. Index Terms—Fibonacci numbers, Hamiltonian graphs, graph embedding, hypercubes, interconnection topologies.
Parallel and Distributed Finite Constraint Satisfaction: Complexity, Algorithms and Experiments
, 1992
"... This paper explores the parallel complexity of finite constraint satisfaction problems (FCSPs) by developing three algorithms for deriving minimal constraint networks in parallel. The first is a parallel algorithm for the EREW PRAM model, the second is a distributed algorithm for finegrain intercon ..."
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Cited by 15 (1 self)
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This paper explores the parallel complexity of finite constraint satisfaction problems (FCSPs) by developing three algorithms for deriving minimal constraint networks in parallel. The first is a parallel algorithm for the EREW PRAM model, the second is a distributed algorithm for finegrain interconnected networks, and the third is a distributed algorithm for coarsegrain interconnected networks. Our major results are: given an FCSP represented by an acyclic constraint network (or a join tree) of size n with treewidth bounded by a constant, then (1) the parallel algorithm takes O(log n) time using O(n) processors, (2) there is an equivalent network, of size poly(n) with treewidth also bounded by a constant, which can be solved by the finegrain distributed algorithm in O(log n) time using poly(n) processors and (3) the distributed algorithm for coarsegrain interconnected networks has linear speedup and linear scaleup. In addition, we have simulated the finegrain distributed algorit...
Optimal Routing of Parentheses on the Hypercube
 IN PROCEEDINGS OF THE SYMPOSIUM ON PARALLEL ARCHITECTURES AND ALGORITHMS
, 1994
"... We consider a new class of routing requests or partial permutations for which we give optimal online routing algorithms on the hypercube and shuffleexchange network. For wellformed words of parentheses our algorithm establishes communication between all matching pairs in logarithmic time. It can ..."
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Cited by 15 (6 self)
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We consider a new class of routing requests or partial permutations for which we give optimal online routing algorithms on the hypercube and shuffleexchange network. For wellformed words of parentheses our algorithm establishes communication between all matching pairs in logarithmic time. It can be applied to the membership problem for Dyck languages and a number of problems for algebraic expressions.