arXiv subjects

Erhan Tezcan

Publications and source records attributed to Erhan Tezcan.

3 recordsLinked to original sources

arXiv2021

Monitoring Collective Communication Among GPUs

Communication among devices in multi-GPU systems plays an important role in terms of performance and scalability. In order to optimize an application, programmers need to know the type and amount of the communication happening among GPUs. Although there are prior works to gather this information in MPI applications on distributed systems and multi-threaded applications on shared memory systems, there is no tool that identifies communication among GPUs. Our prior work, ComScribe, presents a point-to-point (P2P) communication detection tool for GPUs sharing a common host. In this work, we extend ComScribe to identify communication among GPUs for collective and P2P communication primitives in NVIDIA's NCCL library. In addition to P2P communications, collective communications are commonly used in HPC and AI workloads thus it is important to monitor the induced data movement due to collectives. Our tool extracts the size and the frequency of data transfers in an application and visualizes them as a communication matrix. To demonstrate the tool in action, we present communication matrices and some statistics for two applications coming from machine translation and image classification domains.

cs.DC↗

arXiv2019

On Collatz Conjecture

The Collatz Conjecture can be stated as: using the reduced Collatz function $C(n) = (3n+1)/2^x$ where $2^x$ is the largest power of 2 that divides $3n+1$, any odd integer $n$ will eventually reach 1 in $j$ iterations such that $C^j(n) = 1$. In this paper we use reduced Collatz function and reverse reduced Collatz function. We present odd numbers as sum of fractions, which we call `fractional sum notation' and its generalized form `intermediate fractional sum notation', which we use to present a formula to obtain numbers with greater Collatz sequence lengths. We give a formula to obtain numbers with sequence length 2. We show that if trajectory of $n$ is looping and there is an odd number $m$ such that $C^j(m) = 1$, $n$ must be in form $3^j\times2k + 1, k \in \mathbb{N}_0$ where $C^j(n) = n$. We use Intermediate fractional sum notation to show a simpler proof that there are no loops with length 2 other than trivial cycle looping twice. We then work with reverse reduced Collatz function, and present a modified version of it which enables us to determine the result in modulo 6. We present a procedure to generate a Collatz graph using reverse reduced Collatz functions.

math.GM↗

arXiv2019

A Lighthouse Illumination Problem

This paper discusses a problem that consists of $n$ "lighthouses" which are circles with radius 1, placed around a common center, equidistant at $n$ units away from the placement center. Consecutive lighthouses are separated by the same angle: $360^\circ/n$ which we denote as $α$. Each lighthouse "illuminates" facing towards the placement center with the same angle $α$, also called "Illumination Angle" in this case. As for the light source itself, there are two variations: a single point light source at the center of each lighthouse and point light sources on the arc seen by the illumination angle for each lighthouse. The problem: what is the total dark (not illuminated) area for a given number of lighthouses, and as the number of lighthouses approach infinity? We show that by definition of the problem, neighbor lighthouses do not overlap or be tangent to each other. We propose a solution for the center point light source case and discuss several small cases of $n$ for the arc light source case.

math.HO↗