Related papers: Slightly smaller splitter networks

We consider the task of assigning unique integers to a group of processes in an asynchronous distributed system of a total of $n$ processes prone to crashes that communicate through shared read-write registers. In the Renaming problem, an…

The locator/identifier split approach assumes separating functions of a locator (i.e. topology--dependent attachment point address) and identifier (topology-independent unique identifier) currently both served by an IP address. This work is…

The work in this article is concerned with two different types of families of finite sets: separating families and splitting families (they are also called "systems"). These families have applications in combinatorial search, coding theory,…

Local certification is the area of distributed network computing asking the following question: How to certify to the nodes of a network that a global property holds, if they are limited to a local verification? In this area, it is often…

This paper considers computational methods that split a vector field into three components in the case when both the vector field and the split components might be unbounded. We first employ classical Taylor expansion which, after some…

Performance of standard processes over large distributed networks typically scales with the size of the network. For example, in planar topologies where nodes communicate with their natural neighbors, the scaling factor is $O(n)$, where $n$…

For convolutional neural networks (CNNs) that have a large volume of input data, memory management becomes a major concern. Memory cost reduction can be an effective way to deal with these problems that can be realized through different…

In the renaming problem, each process in a distributed system is issued a unique name from a large name space, and the processes must coordinate with one another to choose unique names from a much smaller name space. We show that lower…

A tight lower bound for required I/O when computing an ordinary matrix-matrix multiplication on a processor with two layers of memory is established. Prior work obtained weaker lower bounds by reasoning about the number of segments needed…

Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes…

We adapt the rectangular splitting technique of Paterson and Stockmeyer to the problem of evaluating terms in holonomic sequences that depend on a parameter. This approach allows computing the $n$-th term in a recurrent sequence of suitable…

The splitting number of a link is the minimal number of crossing changes between different components required to convert it into a split link. We obtain a lower bound on the splitting number in terms of the (multivariable) signature and…

We establish that a simple polynomial-time algorithm that we call reweighted spectral partitioning obtains small 2/3-balanced vertex-separators for a number of graph classes, including $O(\sqrt{n})$-sized separators for planar graphs,…

We consider a class of finite state three-tape transducers which models the operation of shuffling and splitting words. We present them as automata over the so-called Shuffling Monoid. These automata can be seen as either shufflers or…

Identifiers and sequence numbers make up a large part of the protocol overhead in certain low-power wide-area networks. The requirement for cryptographic nonces in authentication and encryption schemes often demands excessively long…

Using elementary means, we derive the three most popular splittings of $e^{(A+B)}$ and their error bounds in the case when $A$ and $B$ are (possibly unbounded) operators in a Hilbert space, generating strongly continuous semigroups,…

We revisit the problem of finding small $\epsilon$-separation keys introduced by Motwani and Xu (2008). In this problem, the input is $m$-dimensional tuples $x_1,x_2,\ldots,x_n $. The goal is to find a small subset of coordinates that…

A node separator of a graph is a subset S of the nodes such that removing S and its incident edges divides the graph into two disconnected components of about equal size. In this work, we introduce novel algorithms to find small node…

We suggest a method for routing when the source does not posses full information about the shortest path to the destination. The method is particularly useful for scale-free networks, and exploits its unique characteristics. By assigning…

Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…