Showing papers by "Ming-Yang Kao published in 1994"

Optimal online scheduling of parallel jobs with dependencies

Abstract: We study the following general on-line scheduling problem Paralleljobs arrive on a parallel machine dynamically according to thedependencies between them Each job requests a certain number ofprocessors in a specific communication configuration, but its runningtime is not known until it is completed We present optimal on-linealgorithms for PRAMs and one-dimensional meshes, and efficientalgorithms for hypercubes and general meshes For PRAMs we obtainoptimal tradeoffs between the competitive ratio and the largestnumber of processors requested by any job

Optimal Broadcast in All-Port Wormhole-Routed Hypercubes

Abstract: We give an optimal algorithm that broadcasts on an n-dimensional hypercube in Theta(n/ log_{2}(n+ 1)) routing steps with wormhole, e-cube routing and all-port communication. Previously, the best algorithm of McKinley and Trefftz requires [n/2] routing steps. We also give routing algorithms that achieve tight time bounds for n leqslant 7.

Optimal constructions of hybrid algorithms

Abstract: We study on-line strategies for solving problems with hybrid algorithms. There is a problem Q and w basic algorithms for solving Q. For some � ≤ w, we have a computer withdisjoint memory areas, each of which can be used to run a basic algorithm and store its intermediate results. In the worst case, only one basic algorithm can solve Q in finite time, and all the other basic algorithms run forever without solving Q. To solve Q with a hybrid algorithm constructed from the basic algorithms, we run a basic algorithm for some time, then switch to another, and continue this process until Q is solved. The goal is to solve Q in the least amount of time. Using competitive ratios to measure the efficiency of a hybrid algorithm, we construct an optimal deterministic hybrid algorithm and an efficient randomized hybrid algorithm. This resolves an open question on searching with multiple robots posed by Baeza-Yates, Culberson and Rawlins. We also prove that our randomized algorithm is optimal for � = 1, settling a conjecture of Kao, Reif and Tate.

Regular Edge Labelings and Drawings of Planar Graphs

Abstract: The problems of nicely drawing planar graphs have received increasing attention due to their broad applications [5]. A technique, regular edge labeling, was successfully used in solving several planar graph drawing problems, including visibility representation, straight-line embedding, and rectangular dual problems. A regular edge labeling of a plane graph G labels the edges of G so that the edge labels around any vertex show certain regular pattern. The drawing of G is obtained by using the combinatorial structures resulting from the edge labeling. In this paper, we survey these drawing algorithms and discuss some open problems.

Simple and Efficient Graph Compression Schemes for Dense and Complement Graphs

Abstract: We present two graph compression schemes for solving problems on dense graphs and complement graphs They compress a graph or its complement graph into two kinds of succinct representations based on adjacency intervals and adjacency integers, respectively These two schemes complement each other for different ranges of density Using these schemes, we develop optimal or near optimal algorithms for fundamental graph problems In contrast to previous graph compression schemes, ours are simple and efficient for practical applications

Total Protection of Analytic Invariant Information in Cross Tabulated Tables

Abstract: To protect sensitive information in a cross tabulated table, it is a common practice to suppress some of the cells in the table. An analytic invariant is a power series in terms of the suppressed cells that has a unique feasible value and a convergence radius equal to +∞. Intuitively, the information contained in an invariant is not protected even though the values of the suppressed cells are not disclosed. This paper gives an optimal linear-time algorithm for testing whether there exist nontrivial analytic invariants in terms of the suppressed cells in a given set of suppressed cells. This paper also presents NP-completeness results and an almost lineartime algorithm for the problem of suppressing the minimum number of cells in addition to the sensitive ones so that the resulting table does not leak analytic invariant information about a given set of suppressed cells.

Efficient submesh permutations in wormhole-routed meshes

Abstract: This paper studies how to concurrently permute related logical or physical submeshes in a d -dimensional n × … × n physical mesh via wormhole and dimension-ordered routing. Our objective is to minimize the congestion for realizing the permutations, while maximizing the number and dimensionality of permuted submeshes. We show that for d ⩽ 2 α + β , concurrent independent permutations of n β related physical submeshes, each of α dimensions, can be performed in two routing steps without congestion. If the permuted submeshes are logical ones, they can be permuted in one, instead of two, routing step. In addition, any shift operation along any axis of the logical mesh can be performed in the physical mesh without congestion. We also show that if all nodes know the permutation function, any permutation within a submesh of dimensions ⌊2( d − 1)/3⌋ can be realized in three routing steps without congestion.

Efficient submesh permutations in wormhole-routed meshes

Abstract: This paper studies how to concurrently permute related logical or physical submeshes in a d-dimensional n/spl times/.../spl times/n physical mesh via wormhole and dimension-ordered routing. Our objective is to minimize the congestion for realizing the permutations, while maximizing the number and dimensionality of permuted submeshes. We show that for d/spl les/2/spl alpha/+/spl beta/, concurrent independent permutations of n/sup /spl beta// related physical submeshes, each of /spl alpha/ dimensions, can be performed in two routing steps without congestion. If the permuted submeshes are logical ones, they can be permuted in one, instead of two, routing step. In addition, any shift operation along any axis of the logical mesh can be performed in the physical mesh without congestion. We also show that if all nodes know the permutation function, any permutation within a submesh of dimensions [2(d-1)/3] can be realized in three routing steps without congestion. >