Solution of a Divide-and-Conquer Maximin Recurrence
The solution of the divide-and-conquer recurrence\[ M(n)\mathop {\max }\limits_{1 \leqq k < n} (M(k) + M(n - k) + \min (f(k),f(n - k))) \]is found for a variety of functions f. Asymptotic bounds on $M(n)$ are found for arbitrary nondecreasing f, and the exact form of $M(n)$ is determined for f nondecreasing and weakly concave. As a corollary to the asymptotic bounds, it is shown that $M(n)$ remains linear even when f is almost linear. Among the exact forms determined: For $f(x) = \lfloor {\lg x} \rfloor $, the solution is $M(n) = (M(1) + 1)n - \lfloor {\lg n} \rfloor - \nu (n)$ where $\nu (n)$ is the number of 1-bits in the binary representation of n. For $f(x) = \lfloor {\lg x} \rfloor $, the solution is $M(n) = (M(1) + 1)n - \lceil {\lg n} \rceil - 1$, while for $f(x) = \lceil {\lg (x + 1)} \rceil $, thesolution is $M(n) = (M(1) + 2)n - \lfloor {\lg n} \rfloor - \nu (n) - 1$.

title: New tiling techniques to improve cache temporal locality
abstract: Tiling is a well-known loop transformation to improve temporal locality of nested loops. Current compiler algorithms for tiling are limited to loops which are perfectly nested or can be transformed, in trivial ways, into a perfect nest. This paper presents a number of program transformations to enable tiling for a class of nontrivial imperfectly-nested loops such that cache locality is improved. We define a program model for such loops and develop compiler algorithms for their tiling. We propose to adopt odd-even variable duplication to break anti- and output dependences without unduly increasing the working-set size, and to adopt speculative execution to enable tiling of loops which may terminate prematurely due to, e.g. convergence tests in iterative algorithms. We have implemented these techniques in a research compiler, Panorama. Initial experiments with several benchmark programs are performed on SGI workstations based on MIPS R5K and R10K processors. Overall, the transformed programs run faster by 9% to 164%.

title: A theoretical foundation for program transformations to reduce cache thrashing due to true data sharing
abstract: Cache thrashing due to true data sharing can degrade the performance of parallel programs significantly. Our previous work showed that parallel task alignment via program transformations can be quite effective for the reduction of such cache thrashing. In this paper, we present a theoretical foundation for such program transformations. Based on linear algebra and the theory of numbers, our work analyzes the data dependences among the tasks created by a fork-join parallel program and determines at compile time how these tasks should be assigned to processors in order to reduce cache thrashing due to true data sharing. Our analysis and program transformations can be easily performed by compilers for parallel computers.

title: Compiler algorithms for event variable synchronization
abstract: Event variable synchronization is a well known mecha nism for enforcing data dependences in a program that runs in parallel on a shared memory multiprocessor This paper presents compiler algorithms to automati cally generate event variable synchronization code Pre viously published algorithms dealt with single parallel loops in which dependence distances are constant and known by the compiler However loops in real appli cation programs are often arbitrarily nested Moreover compilers are often unable to determine dependence dis tances In contrast our algorithms generate synchro nization code based directly on array subscripts and do not require constant distances in data dependences The algorithms are designed for arbitrarily nested loops in cluding triangular or trapezoidal loops

title: On Reducing Data Synchronization in Multiprocessed Loops
abstract: In this correspondence we present and prove the correctness of an algorithm for reducing the number of synchronized memory references to shared data elements in multiprocessed loops. Optimizing compilers for shared memory multiprocessors can use this algorithm to reduce synchronization overhead. The algorithm has been implemented as a new module in the multiprocessors version of Parafrase, the restructuring system of the University of Illinois. We present a brief discussion of experiments we performed to asses the effectiveness of this algorithm in reducing the synchronization overhead for the 61 subroutines of EISPACK, a package for computing matrix eigenvectors and eigenvalues.

title: Experience in the Automatic Parallelization of Four Perfect-Benchmark Programs
abstract: This paper discusses the techniques used to hand-parallelize, for the Alliant FX/80, four Fortran programs from the Perfect-Benchmark suite. The paper also includes the execution times of the programs before and after the transformations. The four programs considered here were not effectively parallelized by the automatic translators available to the authors. However, most of the techniques used for hand parallelization, and perhaps all of them, have wide applicability and can be incorporated into existing translators.

title: A parsimonious tree-grow method for haplotype inference
abstract: Haplotype information has become increasingly important in analyzing fine-scale molecular genetics data, such as disease genes mapping and drug design. Parsimony haplotyping is one of haplotyping problems belonging to NP-hard class.



In this paper, we aim to develop a novel algorithm for the haplotype inference problem with the parsimony criterion, based on a parsimonious tree-grow method (PTG). PTG is a heuristic algorithm that can find the minimum number of distinct haplotypes based on the criterion of keeping all genotypes resolved during tree-grow process. In addition, a block-partitioning method is also proposed to improve the computational efficiency. We show that the proposed approach is not only effective with a high accuracy, but also very efficient with the computational complexity in the order of O(m2n) time for n single nucleotide polymorphism sites in m individual genotypes.


AVAILABILITY
The software is available upon request from the authors, or from http://zhangroup.aporc.org/bioinfo/ptg/



chen@elec.osaka-sandai.ac.jp

title: Factoring systems of linear PDEs with finite-dimensional solution spaces
abstract: A D-finite system is a finite set of linear homogeneous partial differential equations in several independent and dependent variables, whose solution space is of finite dimension. Let L be a D-finite system with rational function coefficients. We present an algorithm for computing all hyperexponential solutions of L, and an algorithm for computing all D-finite systems whose coefficients are also rational functions, and whose solutions are contained in the solution space of L.

title: Longest-path selection for delay test under process variation
abstract: Under manufacturing process variation, a path through a fault site is called longest for delay test if there exists a process condition under which the path has the maximum delay among all paths through that fault site. There are often multiple longest paths for each fault site in the circuit, due to different process conditions. To detect the smallest delay fault, it is necessary to test all longest paths through the fault site. However, previous methods are either inefficient or their results include too many paths that are not longest.This paper presents an efficient method to generate the longest path set for delay test under process variation. To capture both structural and systematic process correlation, we use linear delay functions to express path delays under process variation. A novel path-pruning technique is proposed to discard paths that are not longest, resulting in a significantly reduction in the number of paths compared with the previous best method. The new method can be applied to any process variation as long as its impact on delay is linear.

title: Computational Differences between Asymmetrical and Symmetrical Networks
abstract: Symmetrically connected recurrent networks have recently been used as models of a host of neural computations. However, biological neural networks have asymmetrical connections, at the very least because of the separation between excitatory and inhibitory neurons in the brain. We study characteristic differences between asymmetrical networks and their symmetrical counterparts in cases for which they act as selective amplifiers for particular classes of input patterns. We show that the dramatically different dynamical behaviours to which they have access, often make the asymmetrical networks computationally superior. We illustrate our results in networks that selectively amplify oriented bars and smooth contours in visual inputs.

title: A DoS Resilient Flow-level Intrusion Detection Approach for High-speed Networks
abstract: Global-scale attacks like viruses and worms are increasing in frequency, severity and sophistication, making it critical to detect outbursts at routers/gateways instead of end hosts. In this paper we leverage data streaming techniques such as the reversible sketch to obtain HiFIND, a High-speed Flow-level Intrusion Detection system. In contrast to existing intrusion detection systems, HiFIND I ) is scalable to flow-level detection on high-speed networks; 2) zs DoS resilient; 3) can distinguish SYN flooding and various port scans (mostly for worm propagation) for effective mitigation; 4 ) enables aggregate detection over multiple routers/gateways; and 5) separates anomalies to limit false positives in detection. Both theoretical analysis and evaluation with several router traces show that HiFIND achieves these properties. To the best of our knowledge, HiFIND is the first online DoS resilient flow-level intrusion detection system for high-speed networks (approximately 10s of Gigabit/second), even for the worst case trafic of 40-byte-packet streams with each packet forming a flow.