NDLI: The Complexity of Three-Way Statistical Tables

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The Complexity of Three-Way Statistical Tables

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	De Loera, Jesus Onn, Shmuel
Copyright Year	2004
Abstract	Multiway tables with specified marginals arise in a variety of applications in statistics and operations research. We provide a comprehensive complexity classification of three fundamental computational problems on tables: existence, counting, and entry-security.One outcome of our work is that each of the following problems is intractable already for "slim" 3-tables, with constant number 3 of rows: (1) deciding existence of 3-tables with specified 2-marginals; (2) counting all 3-tables with specified 2-marginals; (3) deciding whether a specified value is attained in a specified entry by at least one of the 3-tables having the same 2-marginals as a given table. This implies that a characterization of feasible marginals for such slim tables, sought by much recent research, is unlikely to exist.Another consequence of our study is a systematic efficient way of embedding the set of 3-tables satisfying any given 1-marginals and entry upper bounds in a set of slim 3-tables satisfying suitable 2-marginals with no entry bounds. This provides a valuable tool for studying multi-index transportation problems and multi-index transportation polytopes. Remarkably, it enables us to automatically recover a famous example due to Vlach of a "real-feasible integer-infeasible" collection of 2-marginals for 3-tables of smallest possible size (3,4,6).
Starting Page	819
Ending Page	836
Page Count	18
File Format	PDF
ISSN	00975397
DOI	10.1137/S0097539702403803
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	4
Volume Number	33
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2004-01-01
Access Restriction	Subscribed
Subject Keyword	Frchet bound statistical table data security confidentiality transportation polytope transportation problems statistical disclosure control Combinatorial optimization Contingency tables data quality marginal statistics Analysis of algorithms contingency table computational complexity
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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