Huge multiway table problems

Shmuel Onn

doi:10.1016/j.disopt.2014.07.003

Huge multiway table problems

Shmuel Onn

Data and Decision Sciences

Technion - Israel Institute of Technology

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

Abstract

Optimization over l×m×n integer threeway tables is NP-hard already for fixed l=3, but solvable in polynomial time with both l,m fixed. Here we consider huge tables, where the variable dimension n is encoded in binary. Combining recent results on Graver bases and recent results on integer cones, we show how to handle such problems in polynomial time. We also show that a harder variant of the problem lies in both NP and coNP. Our treatment goes through the more general class of n-fold integer programming problems.

Original language	English
Pages (from-to)	72-77
Number of pages	6
Journal	Discrete Optimization
Volume	14
DOIs	https://doi.org/10.1016/j.disopt.2014.07.003
State	Published - Nov 2014

Keywords

Graver basis
Integer cone
Integer programming
Multiway table

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computational Theory and Mathematics
Applied Mathematics

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10.1016/j.disopt.2014.07.003

Cite this

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abstract = "Optimization over l×m×n integer threeway tables is NP-hard already for fixed l=3, but solvable in polynomial time with both l,m fixed. Here we consider huge tables, where the variable dimension n is encoded in binary. Combining recent results on Graver bases and recent results on integer cones, we show how to handle such problems in polynomial time. We also show that a harder variant of the problem lies in both NP and coNP. Our treatment goes through the more general class of n-fold integer programming problems.",

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doi = "10.1016/j.disopt.2014.07.003",

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AB - Optimization over l×m×n integer threeway tables is NP-hard already for fixed l=3, but solvable in polynomial time with both l,m fixed. Here we consider huge tables, where the variable dimension n is encoded in binary. Combining recent results on Graver bases and recent results on integer cones, we show how to handle such problems in polynomial time. We also show that a harder variant of the problem lies in both NP and coNP. Our treatment goes through the more general class of n-fold integer programming problems.

KW - Graver basis

KW - Integer cone

KW - Integer programming

KW - Multiway table

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DO - 10.1016/j.disopt.2014.07.003

M3 - مقالة

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VL - 14

SP - 72

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JO - Discrete Optimization

JF - Discrete Optimization

ER -

Huge multiway table problems

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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