Sparse Integer Programming Is Fixed-Parameter Tractable
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10511016" target="_blank" >RIV/00216208:11320/25:10511016 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=qPMKx90tYa" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=qPMKx90tYa</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1287/moor.2023.0162" target="_blank" >10.1287/moor.2023.0162</a>
Alternative languages
Result language
angličtina
Original language name
Sparse Integer Programming Is Fixed-Parameter Tractable
Original language description
We study the general integer programming problem where the number of variables n is a variable part of the input. We consider two natural parameters of the constraint matrix A: its numeric measure a and its sparsity measure d. We present an algorithm for solving integer programming in time g(a, d)poly(n, L), where g is some computable function of the parameters a and d, and L is the binary encoding length of the input. In particular, integer programming is fixed-parameter tractable parameterized by a and d, and is solvable in polynomial time for every fixed a and d. Our results also extend to nonlinear separable convex objective functions.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/GA22-22997S" target="_blank" >GA22-22997S: Efficient and Realistic Models in Computational Social Choice</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematics of Operations Research
ISSN
0364-765X
e-ISSN
1526-5471
Volume of the periodical
50
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
16
Pages from-to
2141-2156
UT code for WoS article
001293983300001
EID of the result in the Scopus database
2-s2.0-105014263749