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Fortran is still widely used in scientific computing, and a very large corpus of legacy as well as new code is written in FORTRAN 77. In general this code is not type safe, so that incorrect programs can compile without errors. In this paper, we present a formal approach to ensure type safety of legacy Fortran code through automated program transformation. The objective of this work is to reduce programming errors by guaranteeing type safety. We present the first rigorous analysis of the type safety of FORTRAN 77 and the novel program transformation and type checking algorithms required to convert FORTRAN 77 subroutines and functions into pure, side-effect free subroutines and functions in Fortran 90. We have implemented these algorithms in a source-to-source compiler which type checks and automatically transforms the legacy code. We show that the resulting code is type safe and that the pure, side-effect free and referentially transparent subroutines can readily be offloaded to accelerators. [ABSTRACT FROM AUTHOR]

SpMV (Sparse matrix-vector multiplication) is an essential component in scientific computing and has attracted the attention of researchers in related fields at home and abroad. With the continuous expansion of matrix data, the efficient parallel SpMV algorithm has become a research hotspot for research experts in related fields. The sparse matrix compression format as a critical point to improve computing performance can effectively save storage space and efficiently cooperate with the advantages of the processor system structure to give full play to performance. This paper proposes a new sparse matrix storage format CSR2 (Compressed Sparse Row 2). It is a new single format and suitable for processor platforms with SIMD (Single Instruction Multiple Data) vectorizations. The format operation of CSR2 is easy to implement with a low overhead of conversion. We compared the SpMV algorithm based on CSR2 with the most advanced single format CSR5 (Compressed Sparse Row 5) and Intel MKL (Intel Math Kernel Library) on the mainstream high-performance processor Intel Xeon E5-2670 v3 CPU. We choose 48 sets of matrices to be used as a benchmark suite. Experimental results show that CSR2 has a remarkable performance improvement compared with CSR5 and MKL. Compared to CSR5, CSR2 can achieve an average acceleration of 1.401 × (up to 1.861 ×). Compared to MKL, CSR2 can achieve an average acceleration of 1.261 × (up to 5.921 ×). In reality, for applications with multiple iterations, using our CSR2 can bring low-overhead format conversion and high-throughput computing performance. [ABSTRACT FROM AUTHOR]

Sparse triangular solve (SpTRSV) is an important kernel in many scientific computing applications. In traditional viewpoints, accelerating SpTRSV by parallelizing the solution process is a challenging task. Dependencies among the variables that exist in the solution process not only restrict the parallelism that can be achieved, but also introduce large synchronization overhead among the parallel tasks. Moreover, a time-consuming pre-processing phase is commonly required to identify calculations that can be parallelized. However, we have observed that a large number of dependencies among the variables can be eliminated if we only calculate partial values of the variables first and add them together to obtain the final values later. By using such a strategy, starting to solve a variable does not need to wait for all of its prerequisite variables having been solved. In consequence, parallelism of the SpTRSV can be increased significantly. In this paper, we transform above mentioned observations into a subtree-based parallel algorithm to accelerate SpTRSV. The proposed algorithm calculates partial values of the variable along with an implicit subtree traversal and utilizes hardware atomic operation to implement accumulation of the partial values. This not only introduces no pre-processing overhead, but also avoids any barrier synchronization among the parallel threads. We evaluate the proposed algorithm on 2135 matrices from SuiteSparse Matrix Collection based on a generic GPU platform. Experimental results demonstrate that our scheme outperforms the state-of-the-art GPU and CPU vendor libraries in 1949 and 1782 matrices, respectively. Compared with the latest synchronization-free method, our scheme outperforms in 1779 matrices. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of designing a β -additive fault-tolerant approximate BFS (or FT-ABFS for short) structure, namely, a subgraph H of the network G such that subsequent to the failure of a single edge e, the surviving part of H still contains an approximate BFS spanning tree for (the surviving part of) G, whose distances satisfy dist (s , v , H \ { e }) ≤ dist (s , v , G \ { e }) + β for every v ∈ V . It was shown in Parter and Peleg (SODA, 2014), that for every β ∈ [ 1 , O (log n) ] there exists an n-vertex graph G with a source s for which any β -additive FT-ABFS structure rooted at s has Ω (n 1 + ϵ (β)) edges, for some function ϵ (β) ∈ (0 , 1) . In particular, 3-additive FT-ABFS structures admit a lower bound of Ω (n 5 / 4) edges. In this paper we present the first upper bound, showing that there exists a poly-time algorithm that for every n-vertex unweighted undirected graph G and source s constructs a 4-additive FT-ABFS structure rooted at s with at most O (n 4 / 3) edges. The main technical contribution of our algorithm is in adapting the path-buying strategy used in Baswana et al. (ACM Trans Algorithms 7:A5, 2010) and Cygan et al. (Proceedings of the 30th symposium on theoretical aspects of computer science, pp 209–220, 2013) to failure-prone settings. [ABSTRACT FROM AUTHOR]

Given a graph G, a properk-coloring of G is a partition c = (S i) i ∈ [ 1 , k ] of V(G) into k stable sets S 1 , ... , S k . Given a weight function w : V (G) → R + , the weight of a color S i is defined as w (i) = max v ∈ S i w (v) and the weight of a coloringc as w (c) = ∑ i = 1 k w (i) . Guan and Zhu (Inf Process Lett 61(2):77–81, 1997) defined the weighted chromatic number of a pair (G, w), denoted by σ (G , w) , as the minimum weight of a proper coloring of G. The problem of determining σ (G , w) has received considerable attention during the last years, and has been proved to be notoriously hard: for instance, it is NP-hard on split graphs, unsolvable on n-vertex trees in time n o (log n) unless the ETH fails, and W[1]-hard on forests parameterized by the size of a largest tree. We focus on the so-called dual parameterization of the problem: given a vertex-weighted graph (G, w) and an integer k, is σ (G , w) ≤ ∑ v ∈ V (G) w (v) - k ? This parameterization has been recently considered by Escoffier (in: Proceedings of the 42nd international workshop on graph-theoretic concepts in computer science (WG). LNCS, vol 9941, pp 50–61, 2016), who provided an FPT algorithm running in time 2 O (k log k) · n O (1) , and asked which kernel size can be achieved for the problem. We provide an FPT algorithm in time 9 k · n O (1) , and prove that no algorithm in time 2 o (k) · n O (1) exists under the ETH. On the other hand, we present a kernel with at most (2 k - 1 + 1) (k - 1) vertices, and rule out the existence of polynomial kernels unless NP ⊆ coNP / poly , even on split graphs with only two different weights. Finally, we identify classes of graphs allowing for polynomial kernels, namely interval graphs, comparability graphs, and subclasses of circular-arc and split graphs, and in the latter case we present lower bounds on the degrees of the polynomials. [ABSTRACT FROM AUTHOR]

A large number of free boundary problems can be formulated as linear-complementarity problems. In this paper, we propose an inexact alternating direction method of multipliers for solving linear complementarity problem arising from free boundary problems by using the special structure of these problems. The convergence of our proposed method is proved. Numerical results show that the proposed method is feasible and effective, and it is significantly faster than modified alternating direction implicit algorithm and many other methods, especially when dimension of the problem being solved is large. [ABSTRACT FROM AUTHOR]

The computation of eigenvalues of large-scale matrices arising from finite element discretizations has gained significant interest in the last decade (Knyazev et al. in Numerical solution of PDE eigenvalue problems, vol 56. Mathematisches Forschungsinstitut, Oberwolfach, ). Here we present an new algorithm based on slicing the spectrum that takes advantage of the rank structure of resolvent matrices in order to compute $$m$$ eigenvalues of the generalized symmetric eigenvalue problem in $${\fancyscript{O}}(nm\log ^\alpha n)$$ operations, where $$\alpha >0$$ is a small constant. [ABSTRACT FROM AUTHOR]