A Distributed and Incremental SVD Algorithm for Agglomerative Data Analysis on Large Networks

In this paper, we show that the SVD of a matrix can be constructed efficiently in a hierarchical approach. Our algorithm is proven to recover the singular values and left singular vectors if the rank of the input matrix $A$ is known. Further, the hierarchical algorithm can be used to recover the $d$ largest singular values and left singular vectors with bounded error. We also show that the proposed method is stable with respect to roundoff errors or corruption of the original matrix entries. Numerical experiments validate the proposed algorithms and parallel cost analysis

A General Framework for Static Cost Analysis of Parallel Logic Programs

The estimation and control of resource usage is now an important challenge in an increasing number of computing systems. In particular, requirements on timing and energy arise in a wide variety of applications such as internet of things, cloud computing, health, transportation, and robots. At the same time, parallel computing, with (heterogeneous) multi-core platforms in particular, has become the dominant paradigm in computer architecture. Predicting resource usage on such platforms poses a difficult challenge. Most work on static resource analysis has focused on sequential programs, and relatively little progress has been made on the analysis of parallel programs, or more specifically on parallel logic programs. We propose a novel, general, and flexible framework for setting up cost equations/relations which can be instantiated for performing resource usage analysis of parallel logic programs for a wide range of resources, platforms, and execution models. The analysis estimates both lower and upper bounds on the resource usage of a parallel program (without executing it) as functions on input data sizes. In addition, it also infers other meaningful information to better exploit and assess the potential and actual parallelism of a system. We develop a method for solving cost relations involving the max function that arise in the analysis of parallel programs. Finally, we instantiate our general framework for the analysis of logic programs with Independent AndParallelism, report on an implementation within the CiaoPP system, and provide some experimental results. To our knowledge, this is the first approach to the cost analysis of parallel logic programs

Recurrence extraction for functional programs through call-by-push-value

The main way of analyzing the complexity of a program is that of extracting and solving a recurrence that expresses its running time in terms of the size of its input. We develop a method that automatically extracts such recurrences from the syntax of higher-order recursive functional programs. The resulting recurrences, which are programs in a call-by-name language with recursion, explicitly compute the running time in terms of the size of the input. In order to achieve this in a uniform way that covers both call-by-name and call-by-value evaluation strategies, we use Call-by-Push-Value (CBPV) as an intermediate language. Finally, we use domain theory to develop a denotational cost semantics for the resulting recurrences.Comment: POPL 202