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On Integer Programming, Discrepancy, and Convolution [article]

Klaus Jansen, Lars Rohwedder
2019 arXiv   pre-print
We also present a faster specialized algorithm for testing feasibility of an integer program with few constraints and for this we also give a tight lower bound, which is based on the SETH.  ...  (min, +)-convolution has a trivial quadratic time algorithm and it has been conjectured that this cannot be improved significantly.  ...  Eisenbrand and Weismantel observed that using the Steinitz Lemma (with ℓ ∞ norm) one can solve integer programs efficiently, if all entries of the matrix are small integers.  ... 
arXiv:1803.04744v3 fatcat:2kteb4oetnaojbpjgkgnvbf64u

On Integer Programming and Convolution

Klaus Jansen, Lars Rohwedder, Michael Wagner
2018 Innovations in Theoretical Computer Science  
We also present a faster specialized algorithm for testing feasibility of an integer program with few constraints and for this we also give a tight lower bound, which is based on the SETH.  ...  (min, +)convolution has a trivial quadratic time algorithm and it has been conjectured that this cannot be improved significantly.  ...  On Integer Programming and Convolution Dividing both sides by ∆ −1 we get every constraint (4) -( 5 ) for the correct choice of .  ... 
doi:10.4230/lipics.itcs.2019.43 dblp:conf/innovations/JansenR19 fatcat:53vra2wpmbfk5exurfxvchfmza

Page 702 of Behavior Research Methods Vol. 10, Issue 5 [page]

1978 Behavior Research Methods  
to the raw data points may be selected flexibly from published lists of convolution integers without extensive programming; and (2) the computational requirements of the convolution integers technique  ...  The polynomial order chosen is based on the expected form of the raw data, the selected length of the convolution integer list, and the time that can be allocated for computation.  ... 

Minicomputer processing of dual Purkinje image eye-tracker data

John E. Evans, James C. Gutmann
1978 Behavior Research Methods  
Convolatien integers are used to estimate the velocity and acceleration of eye movements, and these serve as the basis of an eye movement data-classification program.  ...  The technique of derivative estimation by convolution integers has the advantage of being easily calculated and the disadvantage of returning results shifted in phase.  ...  to the raw data points may be selected flexibly from published lists of convolution integers without extensive programming; and (2) the computational requirements of the convolution integers technique  ... 
doi:10.3758/bf03205374 fatcat:uxbe2i5bq5dqvodj62r6rf27gq

Constructive characterizations of the value function of a mixed-integer program II

C.E. Blair, R.G. Jeroslow
1985 Discrete Applied Mathematics  
Gomory functions, value functions of integer programs, and value functions of mixed-integer programs are defined on monoids and are all subadditive on their domains.Theorem 2.6 (see [4, Theorem 6.1]).  ...  One easily proves that only the infimal convolution of functions two-at-a-time need be defined.  ... 
doi:10.1016/0166-218x(85)90045-9 fatcat:jqa4vbvykbddhbveag34ninusm

POSTER: Space and Time Optimal DNN Primitive Selection with Integer Linear Programming

Yuan Wen, Andrew Anderson, Valentin Radu, Michael F.P. OBoyle, David Gregg
2019 2019 28th International Conference on Parallel Architectures and Compilation Techniques (PACT)  
We propose an aheadof-time primitive selection for CNNs, based on integer linear programming (ILP).  ...  Convolutional neural networks (CNNs) are used in many applications, from industrial robotics to biometric identification on mobile devices.  ...  We show that by using an Integer Linear Programming based solver model, hybrid selection of convolutional layer implementations can optimize for both inference latency and memory footprint.  ... 
doi:10.1109/pact.2019.00059 dblp:conf/IEEEpact/Wen0ROG19 fatcat:qmkiufmd5fbn5msgvr3m55luse

Cumulative subject index volumes 56–59

1983 Information and Control  
concurrency theory connections, 57, 102 Monotone network complexity of Boolean convolution, lower bound one 59, 184 Multiplier integer, area-time optimal VLSI: with minimum computation time, 58  ...  and always in program verification, 57, 165 Space GF(q) ~, subspaces of: and convolutional codes, 59, 148 metric, and concurrency theory connec- tions, 57, 102 and time, deterministic context free  ... 
doi:10.1016/s0019-9958(83)80037-0 fatcat:dtwnjwpfbndyfc26jagdqcnmwa

Discrete weighted transforms and large-integer arithmetic

Richard Crandall, Barry Fagin
1994 Mathematics of Computation  
We indicate how these ideas can be applied to enhance known algorithms for general multiplication, division, and factorization oflarge integers.  ...  It is well known that Discrete Fourier Transform (DFT) techniques may be used to multiply large integers.  ...  We wish to acknowledge the aid of Robert Silverman, Samuel Wagstaff, and Peter Montgomery on various factorization and verification issues.  ... 
doi:10.1090/s0025-5718-1994-1185244-1 fatcat:lcckqd5zqzfnxfvzpoh2l4fjhm

Special Aspects of Matrix Operation Implementations for Low-Precision Neural Network Model on the Elbrus Platform

E.E. Limonova, Federal Research Center ", M.I. Neiman-zade, V.L. Arlazarov, Computer Science and Control", of the Russian Academy of Sciences, Smart Engines Service LLC, JSC "MCST", Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences
2020 Bulletin of the South Ural State University Series Mathematical Modelling Programming and Computer Software  
This paper investigates the possibility of effective implementation of calculations in lowprecision neural network models on the Elbrus platform with the VLIW architecture.  ...  Such models are widely used in practice to increase the computational efficiency of recognition and well suit computers with the x86 and ARM architectures.  ...  Such methods allow to use small-sized integer types for the calculations and increase the computational performance on a number of x86, x86_64 and ARM processors.  ... 
doi:10.14529/mmp200109 fatcat:7txfuvur35dovkvkuzsdmixxrm

Discrete Weighted Transforms and Large-Integer Arithmetic

Richard Crandall, Barry Fagin
1994 Mathematics of Computation  
We indicate how these ideas can be applied to enhance known algorithms for general multiplication, division, and factorization oflarge integers.  ...  It is well known that Discrete Fourier Transform (DFT) techniques may be used to multiply large integers.  ...  We wish to acknowledge the aid of Robert Silverman, Samuel Wagstaff, and Peter Montgomery on various factorization and verification issues.  ... 
doi:10.2307/2153411 fatcat:6rbddxlpfjakdkxayak7t46jx4

Software reuse for scientific computing through program generation

Martin Erwig, Zhe Fu
2005 ACM Transactions on Software Engineering and Methodology  
More specifically, we describe the design of a program generator for the specification of subroutines that can be generic in the dimensions of arrays, parameter lists, and called subroutines.  ...  We present a program-generation approach to address a software-reuse challenge in the area of scientific computing.  ...  The Markovian convolution in time is one particular convolution tool defined by the following formula.  ... 
doi:10.1145/1061254.1061257 fatcat:a632prblqbhgvjjmiz4454xypi

Implementation of Integer Wavelet Transform on Software Configurable Processor

Shishir Pandey, U. Niranjan
2006 2006 Annual IEEE India Conference  
We have implemented the integer wavelet transform on the Stretch's Software Configurable Processor (SCP). A comparison of a Pentium based implementation and the SCP based implementation was done.  ...  In this work we propose a faster implementation of the integer wavelet transform used in the JPEG 2000 standard.  ...  In our work we have implemented the convolution based integer wavelet transform on the Stretch's SCP. The processor can be programmed using C language.  ... 
doi:10.1109/indcon.2006.302815 fatcat:x2dqogfxizgpzkpovu23my36ba

Efficient Multiplication of Polynomials on Graphics Hardware [chapter]

Pavel Emeliyanenko
2009 Lecture Notes in Computer Science  
We compared our approach with CPU-based implementations of polynomial and large integer multiplication provided by NTL and GMP 2 libraries.  ...  We present the algorithm to multiply univariate polynomials with integer coefficients efficiently using the Number Theoretic transform (NTT) on Graphics Processing Units (GPU).  ...  We would like to thank Michael Kerber for reviewing the paper and for useful and pragmatic suggestions.  ... 
doi:10.1007/978-3-642-03644-6_11 fatcat:juiyao7s5rhnrnd5sjpgnr6jty

Small programming exercises 18

M. Rem
1987 Science of Computer Programming  
The program has three channels for communication with its environment: input channels a and b and output channel c, all of type integer.  ...  The notation for parallel programs may be called CSP-like [ 11: in its communication actions input and output coincide. The functional programs express functions on (infinite) lists.  ...  Exercise 43: Convolution (parallel) Design a parallel program with communication behaviour Functional programs Our functional program notation is an executable formalism for expressing functions on  ... 
doi:10.1016/0167-6423(87)90027-x fatcat:5zxnd5y245bhnco4gfyaofihum

HAO: Hardware-aware neural Architecture Optimization for Efficient Inference [article]

Zhen Dong, Yizhao Gao, Qijing Huang, John Wawrzynek, Hayden K.H. So, Kurt Keutzer
2021 arXiv   pre-print
Differing from existing hardware-aware neural architecture search (NAS) algorithms that rely solely on the expensive learning-based approaches, our work incorporates integer programming into the search  ...  Given a set of hardware resource constraints, our integer programming formulation directly outputs the optimal accelerator configuration for mapping a DNN subgraph that minimizes latency.  ...  Programming: Given a latency constraint Lat 0 , we use integer programming to obtain feasible neural architectures and corresponding quantization settings.  ... 
arXiv:2104.12766v1 fatcat:wvpt6sil4zhf5dknqhv5zj76lu
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