On line sum optimization

Shmuel Onn

doi:10.1016/j.laa.2020.10.004

On line sum optimization

Shmuel Onn

Data and Decision Sciences

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

We show that the column sum optimization problem, of finding a (0,1)-matrix with prescribed row sums which minimizes the sum of evaluations of given functions at its column sums, can be solved in polynomial time, either when all functions are the same or when all row sums are bounded by any constant. We conjecture that the more general line sum optimization problem, of finding a matrix minimizing the sum of given functions evaluated at its row sums and column sums, can also be solved in polynomial time.

Original language	English
Pages (from-to)	474-479
Number of pages	6
Journal	Linear Algebra and Its Applications
Volume	610
DOIs	https://doi.org/10.1016/j.laa.2020.10.004
State	Published - 1 Feb 2021

Keywords

Column sum
Degree sequence
Graph
Majorization
Matrix
Row sum

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

Access to Document

10.1016/j.laa.2020.10.004

Cite this

@article{314071ad3d6a4100886e6f65d2dcd61a,

title = "On line sum optimization",

abstract = "We show that the column sum optimization problem, of finding a (0,1)-matrix with prescribed row sums which minimizes the sum of evaluations of given functions at its column sums, can be solved in polynomial time, either when all functions are the same or when all row sums are bounded by any constant. We conjecture that the more general line sum optimization problem, of finding a matrix minimizing the sum of given functions evaluated at its row sums and column sums, can also be solved in polynomial time.",

keywords = "Column sum, Degree sequence, Graph, Majorization, Matrix, Row sum",

author = "Shmuel Onn",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2021",

month = feb,

day = "1",

doi = "10.1016/j.laa.2020.10.004",

language = "الإنجليزيّة",

volume = "610",

pages = "474--479",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

}

TY - JOUR

T1 - On line sum optimization

AU - Onn, Shmuel

PY - 2021/2/1

Y1 - 2021/2/1

N2 - We show that the column sum optimization problem, of finding a (0,1)-matrix with prescribed row sums which minimizes the sum of evaluations of given functions at its column sums, can be solved in polynomial time, either when all functions are the same or when all row sums are bounded by any constant. We conjecture that the more general line sum optimization problem, of finding a matrix minimizing the sum of given functions evaluated at its row sums and column sums, can also be solved in polynomial time.

AB - We show that the column sum optimization problem, of finding a (0,1)-matrix with prescribed row sums which minimizes the sum of evaluations of given functions at its column sums, can be solved in polynomial time, either when all functions are the same or when all row sums are bounded by any constant. We conjecture that the more general line sum optimization problem, of finding a matrix minimizing the sum of given functions evaluated at its row sums and column sums, can also be solved in polynomial time.

KW - Column sum

KW - Degree sequence

KW - Graph

KW - Majorization

KW - Matrix

KW - Row sum

UR - http://www.scopus.com/inward/record.url?scp=85092620112&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2020.10.004

DO - 10.1016/j.laa.2020.10.004

M3 - مقالة

SN - 0024-3795

VL - 610

SP - 474

EP - 479

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

On line sum optimization

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Cite this