EREW Research Articles

Effectively utilizing global cluster memory for large data-intensive parallel programs

Large scientific parallel applications demand large amounts of memory space. Current parallel computing platforms schedule jobs without fully knowing their memory requirements. This leads to uneven memory allocation in which some nodes are overloaded. This, in turn, leads to disk paging, which is extremely expensive in the context of scientific parallel computing. To solve this problem, we propose a new peer-to-peer solution called parallel network RAM. This approach avoids the use of disk, better utilizes available RAM resources, and will allow larger problems to be solved while reducing the computational, communication, and synchronization overhead typically involved in parallel applications. We proposed several different parallel network RAM designs and evaluated the performance of each under different conditions. We discovered that different designs are appropriate in different situations.

ARITHMETIC CODING IN PARALLEL

We present an EREW PRAM cost optimal parallel algorithm for arithmetic coding computation. We solve the problem in [Formula: see text] time using n/log n processors. Each part of the algorithm as well as a well-known parallel prefix computation forming a basis of the algorithm are clarified on simple examples.

The Hamiltonian problem on distance-hereditary graphs

In this paper, we first present an O ( n + m ) -time sequential algorithm to solve the Hamiltonian problem on a distance-hereditary graph G, where n and m are the number of vertices and edges of G, respectively. This algorithm is faster than the previous best known algorithm for the problem which takes O ( n 2 ) time. We also give an efficient parallel implementation of our sequential algorithm. Moreover, if G is represented by its decomposition tree form, the problem can be solved optimally in O ( log n ) time using O ( ( n + m ) / log n ) processors on an EREW PRAM.

Efficient parallel algorithm to compute a doubly perfect elimination ordering of a doubly chordal graph

The class of doubly chordal graphs, which is a subclass of chordal graphs and a superclass of strongly chordal graphs, arises in many application areas. Many NP-complete optimization problems on chordal graphs like domination and Steiner tree can be solved in polynomial time on doubly chordal graphs using doubly perfect elimination ordering of vertices. In this paper, we show that the computation of a doubly perfect elimination ordering in a doubly chordal graph with n vertices and m edges can be done in O ( log 2 n ) time using O ( n + m ) processors on the CRCW PRAM model.

Parallel recognition algorithms for chordal_planar graphs and planar [formula omitted]-trees

This paper presents parallel algorithms for recognizing chordal_planar graphs and planar k -trees. Both the algorithms run in O ( log 2 n ) time using O ( n + m ) processors on a concurrent-read and concurrent-write (CRCW), parallel random access machine (PRAM) model, where n and m are, respectively, the number of nodes and edges in the graph.The novelty of our chordal_planar graph recognition algorithm lies in that it is based on an elegant structural characterization of chordal_planar graphs proposed in this paper. Moreover, it is simpler than separately testing chordality and planarity. Our planar k-trees recognition algorithm is based on a new characterization of k-trees presented in this paper.

Efficient parallel recognition of cographs

In this paper, we establish structural properties for the class of complement reducible graphs or cographs, which enable us to describe efficient parallel algorithms for recognizing cographs and for constructing the cotree of a graph if it is a cograph; if the input graph is not a cograph, both algorithms return an induced P 4 . For a graph on n vertices and m edges, both our cograph recognition and cotree construction algorithms run in O ( log 2 n ) time and require O ( ( n + m ) / log n ) processors on the EREW PRAM model of computation. Our algorithms are motivated by the work of Dahlhaus (Discrete Appl. Math. 57 (1995) 29–44) and take advantage of the optimal O ( log n ) -time computation of the co-connected components of a general graph (Theory Comput. Systems 37 (2004) 527–546) and of an optimal O ( log n ) -time parallel algorithm for computing the connected components of a cograph, which we present. Our results improve upon the previously known linear-processor parallel algorithms for the problems (Discrete Appl. Math. 57 (1995) 29–44; J. Algorithms 15 (1993) 284–313): we achieve a better time-processor product using a weaker model of computation and we provide a certificate (an induced P 4 ) whenever our algorithms decide that the input graphs are not cographs.

Efficient parallel factorization and solution of structured and unstructured linear systems

This paper gives improved parallel methods for several exact factorizations of some classes of symmetric positive definite (SPD) matrices. Our factorizations also provide us similarly efficient algorithms for exact computation of the solution of the corresponding linear systems (which need not be SPD), and for finding rank and determinant magnitude. We assume the input matrices have entries that are rational numbers expressed as a ratio of integers with at most a polynomial number of bits β . We assume a parallel random access machine (PRAM) model of parallel computation, with unit cost arithmetic operations, including division, over a finite field Z p , where p is a prime number whose binary representation is linear in the size of the input matrix and is randomly chosen by the algorithm. We require only bit precision O ( n ( β + log n ) ) , which is the asymptotically optimal bit precision for β ⩾ log n . Our algorithms are randomized, giving the outputs with high likelihood ⩾ 1 - 1 / n Ω ( 1 ) . We compute LU and QR factorizations for dense matrices, and LU factorizations of sparse matrices which are s ( n ) -separable, reducing the known parallel time bounds for these factorizations from Ω ( log 3 n ) to O ( log 2 n ) , without an increase in processors (matching the best known work bounds of known parallel algorithms with polylog time bounds). Using the same parallel algorithm specialized to structured matrices, we compute LU factorizations for Toeplitz matrices and matrices of bounded displacement rank in time O ( log 2 n ) with n log log n processors, reducing by a nearly linear factor the best previous processor bounds for polylog times (however, these prior works did not generally require unit cost division over a finite field). We use this result to solve in the same bounds: polynomial resultant; and Padé approximants of rational functions; and in a factor O ( log n ) more time: polynomial greatest common divisors (GCD) and extended GCD; again reducing the best processor bounds by a nearly linear factor.

An efficient pram algorithm for maximum-weight independent set on permutation graphs

An efficient parallel algorithm is presented to find a maximum weight independent set of a permutation graph which takesO (logn) time usingO (n 2/logn) processors on an EREW PRAM, provided the graph has at mostO (n) maximal independent sets. The best known parallel algorithm takesO (log2 n) time andO (n 3/logn) processors on a CREW PRAM.

An optimal parallel algorithm for solving all-pairs shortest paths problem on circular-arc graphs

The shortest-paths problem is a fundamental problem in graph theory and finds diverse applications in various fields. This is why shortest path algorithms have been designed more thoroughly than any other algorithm in graph theory. A large number of optimization problems are mathematically equivalent to the problem of finding shortest paths in a graph. The shortest-path between a pair of vertices is defined as the path with shortest length between the pair of vertices. The shortest path from one vertex to another often gives the best way to route a message between the vertices. This paper presents anO(n2) time sequential algorithm and anO(n2/p+logn) time parallel algorithm on EREW PRAM model for solving all pairs shortest paths problem on circular-arc graphs, wherep andn represent respectively the number of processors and the number of vertices of the circular-arc graph.

An optimal parallel algorithm for c-vertex-ranking of trees

For a positive integer c, a c-vertex-ranking of a graph G = ( V , E ) is a labeling of the vertices of G with integers such that, for any label i, deletion of all vertices with labels > i leaves connected components, each having at most c vertices with label i. The c-vertex-ranking problem is to find a c-vertex-ranking of a given graph using the minimum number of ranks. In this paper we give an optimal parallel algorithm for solving the c-vertex-ranking problem on trees in O ( log 2 n ) time using linear number of operations on the EREW PRAM model.

Deleting keys of B-trees in parallel

The B-tree is a fundamental data structure that is used to access and update a large number of keys. In this paper, we present a parallel algorithm on the EREW PRAM that deletes keys in a B-tree. Our algorithm runs in O(B(logk+logBn)) time with k processors, where n is the number of keys in the B-tree, B is the minimum degree of the B-tree, and k is the number of unsorted keys to delete, and it improves upon the previous algorithm by a factor of B.

ALMOST WORK-OPTIMAL PRAM EREW DECODERS OF LZ COMPRESSED TEXT

We show nearly work-optimal parallel decoding algorithms which run on the PRAM EREW in O ( log n) time with O (n/( log n)1/2) processors for text compressed with LZ1 and LZ2 methods, where n is the length of the output string. We also present pseudo work-optimal PRAM EREW decoders for finite window compression and LZ2 compression requiring logarithmic time with O (dn) work, where d is the window size and the alphabet size respectively. Finally, we observe that PRAM EREW decoders requiring O ( log n) time and O (n/ log n) processors are possible with the non-conservative assumption that the computer word length is O ( log 2 n) bits.

Finding r-dominating sets and p-centers of trees in parallel

Let T=(V, E) be an edge-weighted tree with |V|=n vertices embedded in the Euclidean plane. Let IE denote the set of all points on the edges of T. Let X and Y be two subsets of IE and let r be a positive real number. A subset D/spl sube/X is an X/Y/r-dominating set if every point in Y is within distance r of a point in D. The X/Y/r-dominating set problem is to find an X/Y/r-dominating set D* with minimum cardinality. Let p/spl ges/1 be an integer. The X/Y/p-center problem is to find a subset C*/spl sube/X of p points such that the maximum distance of any point in Y from C* is minimized. Let X and Y be either V or IE. In this paper, efficient parallel algorithms on the EREW PRAM are first presented for the X/Y/r-dominating set problem. The presented algorithms require O(log/sup 2/n) time for all cases of X and Y. Parallel algorithms on the EREW PRAM are then developed for the X/Y/p-center problem. The presented algorithms require O(log/sup 3/n) time for all cases of X and Y. Previously, sequential algorithms for these two problems had been extensively studied in the literature. However, parallel solutions with polylogarithmic time existed only for their special cases. The algorithms presented in this paper are obtained by using an interesting approach which we call the dependency-tree approach. Our results are examples of parallelizing sequential dynamic-programming algorithms by using the approach.

A modular integer GCD algorithm

This paper describes the first algorithm to compute the greatest common divisor (GCD) of two n-bit integers using a modular representation for intermediate values U, V and also for the result. It is based on a reduction step, similar to one used in the accelerated algorithm [T. Jebelean, A generalization of the binary GCD algorithm, in: ISSAC '93: International Symposium on Symbolic and Algebraic Computation, Kiev, Ukraine, 1993, pp. 111–116; K. Weber, The accelerated integer GCD algorithm, ACM Trans. Math. Softw. 21 (1995) 111–122] when U and V are close to the same size, that replaces U by ( U − b V ) / p , where p is one of the prime moduli and b is the unique integer in the interval ( − p / 2 , p / 2 ) such that b ≡ U V −1 ( mod p ) . When the algorithm is executed on a bit common CRCW PRAM with O ( n log n log log log n ) processors, it takes O ( n ) time in the worst case. A heuristic model of the average case yields O ( n / log n ) time on the same number of processors.

An efficient parallel strategy for the two-fixed-endpoint Hamiltonian path problem on distance-hereditary graphs

In this paper, we solve the two-fixed-endpoint Hamiltonian path problem on distance-hereditary graphs efficiently in parallel. Let T d (| V|,| E|) and P d (| V|,| E|) denote the parallel time and processor complexities, respectively, required to construct a decomposition tree of a distance-hereditary graph G=( V, E) on a PRAM model M d . We show that this problem can be solved in O( T d (| V|,| E|)+log| V|) time using O( P d (| V|,| E|)+(| V|+| E|)/log| V|) processors on M d . Moreover, if G is represented by its decomposition tree form, the problem can be solved optimally in O(log| V|) time using O((| V|+| E|)/log| V|) processors on an EREW PRAM. We also obtain a linear-time algorithm which is faster than the previous known O(| V| 3) sequential algorithm.

An efficient parallel strategy for the two-fixed-endpoint Hamiltonian path problem on distance-hereditary graphs

In this paper, we solve the two-fixed-endpoint Hamiltonian path problem on distance-hereditary graphs efficiently in parallel. Let T d (| V |,| E |) and P d (| V |,| E |) denote the parallel time and processor complexities, respectively, required to construct a decomposition tree of a distance-hereditary graph G =( V , E ) on a PRAM model M d . We show that this problem can be solved in O ( T d (| V |,| E |)+log| V |) time using O ( P d (| V |,| E |)+(| V |+| E |)/log| V |) processors on M d . Moreover, if G is represented by its decomposition tree form, the problem can be solved optimally in O (log| V |) time using O ((| V |+| E |)/log| V |) processors on an EREW PRAM. We also obtain a linear-time algorithm which is faster than the previous known O (| V | 3 ) sequential algorithm.

Empirical Studies of Optimization Techniques in the Event-Driven Simulation of Mechanically Alloyed Materials

Results of empirical studies of four algorithms for collision detection optimization (CDO) in a framework of event-driven simulation of mechanically alloyed materials are presented. Performance analysis is conducted in a framework of a shaker ball mill model. The results of the study provide insights on how the physical characteristics of the modeled system, such as the number of particles, the distribution of their radii and the density of packing, influence the simulation. Algorithms presented are suitable for parallelization on EREW PRAM architecture with p processors.

Probabilistic integer sorting

We introduce a probabilistic sequential algorithm for stable sorting n uniformly distributed keys in an arbitrary range. The algorithm runs in linear time and sorts all but a very small fraction 2 − Ω(n) of the input sequences; the best previously known bound was 2 − Ω(n/( lgn lglgn)) . An EREW PRAM extension of this sequential algorithm sorts in O(( n/ p+lg p)lg n/lg( n/ p+lg n)) time using p⩽ n processors under the same probabilistic conditions. For a CRCW PRAM we improve upon the probabilistic bound of 2 − Ω(n/( lgn lglgn)) obtained by Rajasekaran and Sen to derive a 2 − Ω(n lglgn/ lgn) bound. Additionally, we present experimental results for the sequential algorithm that establish the practicality of our method.

A practical access to the theory of parallel algorithms

We describe a parallel programming environment that implements the PRAM (Parallel Random Access Machine) model. The programming environment consists of a C-based PRAM programming language called FORK with a compiler, libraries and tools, and a fast PRAM simulator. The software is freely available for Unix workstations. The programming environment and a systematic way of writing structured parallel programs for the PRAM model are described in a recent textbook.Even though the programming environment was originally developed for a hardware research project, we show that the system is also especially suited for complementing classical theory courses on PRAM algorithms by programming exercises that allow students to experiment with PRAM-style parallelism and actually implement the algorithms as they appear in the theory textbooks.We describe how the environment was used in a recent graduate-level course on parallel algorithms, and report on feedback that we got from the participants.

Parallel Algorithms for Recognizing P5-free and ${\bar P}_5$-free Weakly Chordal Graphs

We prove algorithmic characterizations of weakly chordal graphs, which lead to efficient parallel algorithms for recognizing P5-free and [Formula: see text]-free weakly chordal graphs. For an input graph on n vertices and m edges, our algorithms run in O( log 2n) time and require O(m2/ log n) processors on the EREW PRAM model of computation. The proposed recognition algorithms efficiently detect P5 s and [Formula: see text] in weakly chordal graphs in O( log n) time with O(m2/ log n) processors on the EREW PRAM. Additionally, we show how the algorithms can be augmented to provide a certificate for the existence of a P5 (or a [Formula: see text]) in case the input graph is not P5-free (respectively, [Formula: see text]-free) weakly chordal.