Related papers: Sorting Networks: to the End and Back Again

We introduce a sorting machine consisting of $k+1$ stacks in series: the first $k$ stacks can only contain elements in decreasing order from top to bottom, while the last one has the opposite restriction. This device generalizes \cite{SM},…

A sorting network is a shortest path from 12...n to n...21 in the Cayley graph of S_n generated by nearest-neighbour swaps. We prove that for a uniform random sorting network, as n->infinity the space-time process of swaps converges to the…

A new family of graphs, {\it entangled networks}, with optimal properties in many respects, is introduced. By definition, their topology is such that optimizes synchronizability for many dynamical processes. These networks are shown to have…

To address growth challenges facing large Data Centers and supercomputing clusters a new construction is presented for scalable, high throughput, low latency networks. The resulting networks require 1.5-5 times fewer switches, 2-6 times…

This paper describes a computer-assisted non-existence proof of nine-input sorting networks consisting of 24 comparators, hence showing that the 25-comparator sorting network found by Floyd in 1964 is optimal. As a corollary, we obtain that…

We propose and study a strategic model of hiding in a network, where the network designer chooses the links and his position in the network facing the seeker who inspects and disrupts the network. We characterize optimal networks for the…

We consider the problem of selecting $k$ seed nodes in a network to maximize the minimum probability of activation under an independent cascade beginning at these seeds. The motivation is to promote fairness by ensuring that even the least…

This paper introduces a new architectural framework, known as input fast-forwarding, that can enhance the performance of deep networks. The main idea is to incorporate a parallel path that sends representations of input values forward to…

We introduce evolving networks where new vertices preferentially connect to the more central parts of a network. This makes such networks compact. Finite networks grown under the preferential compactness mechanism have complex…

In this paper a new method for checking the subsumption relation for the optimal-size sorting network problem is described. The new approach is based on creating a bipartite graph and modelling the subsumption test as the problem of…

Recent work by Google DeepMind introduced assembly-optimized sorting networks that achieve faster performance for small fixed-size arrays (3-8). In this research, we investigate the integration of these networks as base cases in classical…

One of the fundamental problem in the theory of sorting is to find the pessimistic number of comparisons sufficient to sort a given number of elements. Currently 16 is the lowest number of elements for which we do not know the exact value.…

We engineer algorithms for sorting huge data sets on massively parallel machines. The algorithms are based on the multiway merging paradigm. We first outline an algorithm whose I/O requirement is close to a lower bound. Thus, in contrast to…

In this paper we introduce a new neural architecture for sorting unordered sequences where the correct sequence order is not easily defined but must rather be inferred from training data. We refer to this architecture as OrderNet and…

We consider a stack sorting algorithm where only the appropriate output values are popped from the stack and then any remaining entries in the stack are run through the stack in reverse order. We identify the basis for the $2$-reverse pass…

The back-pressure algorithm is a well-known throughput-optimal algorithm. However, its delay performance may be quite poor even when the traffic load is not close to network capacity due to the following two reasons. First, each node has to…

This paper shows an application of the theory of sorting networks to facilitate the synthesis of optimized general purpose sorting libraries. Standard sorting libraries are often based on combinations of the classic Quicksort algorithm with…

We introduce provenance networks, a novel class of neural models designed to provide end-to-end, training-data-driven explainability. Unlike conventional post-hoc methods, provenance networks learn to link each prediction directly to its…

One approach for reducing run time and improving efficiency of machine learning is to reduce the convergence rate of the optimization algorithm used. Shuffling is an algorithm technique that is widely used in machine learning, but it only…

Distributed network optimization has been studied for well over a decade. However, we still do not have a good idea of how to design schemes that can simultaneously provide good performance across the dimensions of utility optimality,…