A Lower Bound Technique for Communication in BSP

Communication is a major factor determining the performance of algorithms on current computing systems; it is therefore valuable to provide tight lower bounds on the communication complexity of computations. This paper presents a lower bound technique for the communication complexity in the bulk-synchronous parallel (BSP) model of a given class of DAG computations. The derived bound is expressed in terms of the switching potential of a DAG, that is, the number of permutations that the DAG can realize when viewed as a switching network. The proposed technique yields tight lower bounds for the fast Fourier transform (FFT), and for any sorting and permutation network. A stronger bound is also derived for the periodic balanced sorting network, by applying this technique to suitable subnetworks. Finally, we demonstrate that the switching potential captures communication requirements even in computational models different from BSP, such as the I/O model and the LPRAM

Optimized Merge Sort on Modern Commodity Multi-core CPUs

Sorting is a kind of widely used basic algorithms. As the high performance computing devices are increasingly common, more and more modern commodity machines have the capability of parallel concurrent computing. A new implementation of sorting algorithms is proposed to harness the power of newer SIMD operations and multi-core computing provided by modern CPUs. The algorithm is hybrid by optimized bitonic sorting network and multi-way merge. New SIMD instructions provided by modern CPUs are used in the bitonic network implementation, which adopted a different method to arrange data so that the number of SIMD operations is reduced. Balanced binary trees are used in multi-way merge, which is also different with former implementations. Efforts are also paid on minimizing data moving in memory since merge sort is a kind of memory-bound application. The performance evaluation shows that the proposed algorithm is twice as fast as the sort function in C++ standard library when only single thread is used. It also outperforms radix sort implemented in Boost library

The pp-Center Problem in Tree Networks Revisited

We present two improved algorithms for weighted discrete $p$-center problem for tree networks with $n$ vertices. One of our proposed algorithms runs in $O(n \log n + p \log^2 n \log(n/p))$ time. For all values of $p$, our algorithm thus runs as fast as or faster than the most efficient $O(n\log^2 n)$ time algorithm obtained by applying Cole's speed-up technique [cole1987] to the algorithm due to Megiddo and Tamir [megiddo1983], which has remained unchallenged for nearly 30 years. Our other algorithm, which is more practical, runs in $O(n \log n + p^2 \log^2(n/p))$ time, and when $p=O(\sqrt{n})$ it is faster than Megiddo and Tamir's $O(n \log^2n \log\log n)$ time algorithm [megiddo1983]

Faster 3-Periodic Merging Networks

We consider the problem of merging two sorted sequences on a comparator network that is used repeatedly, that is, if the output is not sorted, the network is applied again using the output as input. The challenging task is to construct such networks of small depth. The first constructions of merging networks with a constant period were given by Kuty{\l}owski, Lory\'s and Oesterdikhoff. They have given $3$-periodic network that merges two sorted sequences of $N$ numbers in time $12\log N$ and a similar network of period $4$ that works in $5.67\log N$. We present a new family of such networks that are based on Canfield and Williamson periodic sorter. Our $3$-periodic merging networks work in time upper-bounded by $6\log N$. The construction can be easily generalized to larger constant periods with decreasing running time, for example, to $4$-periodic ones that work in time upper-bounded by $4\log N$. Moreover, to obtain the facts we have introduced a new proof technique