Related papers: Faster Small-Constant-Periodic Merging Networks

In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…

In this paper, we analyse the dual pivot Quicksort, a variant of the standard Quicksort algorithm, in which two pivots are used for the partitioning of the array. We are solving recurrences of the expected number of key comparisons and…

Network pruning is widely used to lighten and accelerate neural network models. Structured network pruning discards the whole neuron or filter, leading to accuracy loss. In this work, we propose a novel concept of neuron merging applicable…

In recent years, hardware implementations of Ising machines have emerged as a viable alternative to quantum computing for solving hard optimization problems among other applications. Unlike quantum hardware, dense connectivity can be…

This paper studies new properties of the front and back ends of a sorting network, and illustrates the utility of these in the search for new bounds on optimal sorting networks. Search focuses first on the "outsides" of the network and then…

A new set of hardware merge sort devices are introduced here, which merge multiple sorted input lists into a single sorted output list in a fast and efficient manner. In each merge sorter, the values from the sorted input lists are arranged…

The problem of merging sorted lists in the least number of pairwise comparisons has been solved completely only for a few special cases. Graham and Karp \cite{taocp} independently discovered that the tape merge algorithm is optimal in the…

Sequential algorithms for the Stable Matching Problem are often too slow in the context of some large scale applications like switch scheduling. Parallel architectures can offer a notable decrease in runtime complexity. We propose a stable…

High order networks are weighted hypergraphs col- lecting relationships between elements of tuples, not necessarily pairs. Valid metric distances between high order networks have been defined but they are difficult to compute when the…

A new Combined Sieve algorithm is presented with cost proportional to the number of enumerated factors over a series of intervals. This algorithm achieves a significant speedup, over a traditional sieve, when handling many ([10^4, 10^7])…

We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the…

We describe a novel extension of subspace codes for noncoherent networks, suitable for use when the network is viewed as a communication system that introduces both dimension and symbol errors. We show that when symbol erasures occur in a…

Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…

The parallel computational complexity or depth of growing network models is investigated. The networks considered are generated by preferential attachment rules where the probability of attaching a new node to an existing node is given by a…

In this article, we take a closer look at the reliability of large minimal networks constructed by repeated compositions of the simplest possible networks. For a given number of devices $n=2^m$ we define the set of all the possible…

We consider the problem of sorting $n$ items, given the outcomes of $m$ pre-existing comparisons. We present a simple and natural deterministic algorithm that runs in $O(m + \log T)$ time and does $O(\log T)$ comparisons, where $T$ is the…

Fast matrix multiplication algorithms may be useful, provided that their running time is good in practice. Particularly, the leading coefficient of their arithmetic complexity needs to be small. Many sub-cubic algorithms have large leading…

Iterative graph algorithms often compute intermediate values and update them as computation progresses. Updated output values are used as inputs for computations in current or subsequent iterations; hence the number of iterations required…

In this work and the supporting Parts II [2] and III [3], we provide a rather detailed analysis of the stability and performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We…

String sorting is an important part of tasks such as building index data structures. Unfortunately, current string sorting algorithms do not scale to massively parallel distributed-memory machines since they either have latency (at least)…