Kwan Woo Ryu

The block distributed memory model

We introduce a computation model for developing and analyzing parallel algorithms on distributed memory machines. The model allows the design of algorithms using a single address space and does not assume any particular interconnection topology. We capture performance by incorporating a cost measure for interprocessor communication induced by remote memory accesses. The cost measure includes parameters reflecting memory latency, communication bandwidth, and spatial locality. Our model allows the initial placement of the input data and pipelined prefetching. We use our model to develop parallel algorithms for various data rearrangement problems, load balancing, sorting, FFT, and matrix multiplication. We show that most of these algorithms achieve optimal or near optimal communication complexity while simultaneously guaranteeing an optimal speed-up in computational complexity. Ongoing experimental work in testing and evaluating these algorithms has thus far shown very promising results.

Load balancing and routing on the hypercube and related networks

Several results related to the load balancing problem on the hypercube, the shuffle-exchange, the cube-connected cycles, and the butterfly are shown. Implications of these results for routing algorithms are also discussed. Our results include the following: • ⊎ Efficient load balancing algorithms are found for the hypercube, the shuffle-exchange, the cube-connected cycles, and the butterfly. • ⊎ Load balancing is shown to require more time on a p-processor shuffle-exchange, cube-connected cycle or butterfly than on a p-processor weak hypercube. • ⊎ Routing n packets on a p-processor hypercube can be done optimally whenever n = p1+1/k, for any fixed k > 0.

Efficient algorithms for list ranking and for solving graph problems on the hypercube

A hypercube algorithm to solve the list ranking problem is presented. Let n be the length of the list, and let p be the number of processors of the hypercube. The algorithm described runs in time O(n/p) when n= Omega (p/sup 1+ epsilon /) for any constant epsilon >0, and in time O(n log n/p+log/sup 3/ p) otherwise. This clearly attains a linear speedup when n= Omega (p/sup 1+ epsilon /). Efficient balancing and routing schemes had to be used to achieve the linear speedup. The authors use these techniques to obtain efficient hypercube algorithms for many basic graph problems such as tree expression evaluation, connected and biconnected components, ear decomposition, and st-numbering. These problems are also addressed in the restricted model of one-port communication. >

The block distributed memory model for shared memory multiprocessors

Introduces a computation model for developing and analyzing parallel algorithms on distributed memory machines. The model allows the design of algorithms using a single address space and does not assume any particular interconnection topology. We capture performance by incorporating a cost measure for interprocessor communication induced by remote memory accesses. The cost measure includes parameters reflecting memory latency, communication bandwidth, and spatial locality. Our model allows the initial placement of the input data and pipelined prefetching. We use our model to develop parallel algorithms for various data rearrangement problems, load balancing, sorting, FFT, and matrix multiplication. We show that most of these algorithms achieve optimal or near optimal communication complexity while simultaneously guaranteeing an optimal speed-up in computational complexity.<<ETX>>

Sorting strings and constructing digital search trees in parallel

We describe two simple optimal-work parallel algorithms for sorting a list L= (X1, X2, …, Xm) of m strings over an arbitrary alphabet Σ, where ∑i = 1m¦Xi¦ = n and two elements of Σ can be compared in unit time using a single processor. The first algorithm is a deterministic algorithm that runs in O(log2m/log log m) time and the second is a randomized algorithm that runs in O(logm) time. Both algorithms use O(m log m + n) operations. Compared to the best-known parallel algorithms for sorting strings, our algorithms offer the following improvements. 1. 1. The total number of operations used by our algorithms is optimal while all previous parallel algorithms use a nonoptimal number of operations. 2. 2. We make no assumption about the alphabet while the previous algorithms assume that the alphabet is restricted to {1, 2, …, no(1)}. 3. 3. The computation model assumed by our algorithms is the Common CRCW PRAM unlike the known algorithms that assume the Arbitrary CRCW PRAM. 4. 4. Our algorithms use O(m log m + n) space, while the previous parallel algorithms use O(n1 + e) space, where e is a positive constant. We also present optimal-work parallel algorithms to construct a digital search tree for a given set of strings and to search for a string in a sorted list of strings. We use our parallel sorting algorithms to solve the problem of determining a minimal starting point of a circular string with respect to lexicographic ordering. Our solution improves upon the previous best-known result to solve this problem.

Optimal algorithms on the pipelined hypercube and related networks

Parallel algorithms for several important combinatorial problems such as the all nearest smaller values problem, triangulating a monotone polygon, and line packing are presented. These algorithms achieve linear speedups on the pipelined hypercube, and provably optimal speedups on the shuffle-exchange and the cube-connected-cycles for any number p of processors satisfying 1 >

An efficient parallel algorithm for the single function coarsest partition problem

We describe an efficient parallel algorithm to solve the single function coarsest partition problem. The algorithm runs in O (log n) time using O(n log log n) operations on the arbitrary CRCW PRAM. The previous best-known algorithms run in O(log2 n) time using O(n log2n) operations on the CREW PRAM, and O(log n) time using O (n log n) operations on the arbitrary CRCW PRAM. Our solution is based on efficient algorithms for solving several subproblems that are of independent interest. In particular, we present efficient parallel algorithms to find a minimal starting point of a circular string with respect to lexicographic ordering and to sort lexicographically a list of strings of different lengths.