The Complexity of Three-Way Statistical Tables

Finite phylogenetic complexity and combinatorics of tables

We prove that the phylogenetic complexity -- an invariant introduced by Sturmfels and Sullivant -- of any finite abelian group is finite.

The Computational Complexity of Rules for the Character Table of S_n

The Murnaghan-Nakayama rule is the classical formula for computing the character table of S_n. Y. Roichman has recently discovered a rule for the Kazhdan-Lusztig characters of q-Hecke algebras of type A, which can also be used for the character table of S_n. For each of the two rules, we give an algorithm for computing entries in the character table of S_n. We then analyze the computational complexity of the two algorithms, and in the case of characters indexed by partitions in the (k,l)-hook, compare their complexities to each other. It turns out that the algorithm based on the Murnaghan-Naka…

Revising Johnson's table for the 21st century

What does it mean today to study a problem from a computational point of view? We focus on parameterized complexity and on Column 16 "Graph Restrictions and Their Effect" of D. S. Johnson's Ongoing guide, where several puzzles were proposed in a summary table with 30 graph classes as rows and 11 problems as columns. Several of the 330 entries remain unclassified into Polynomial or NP-complete after 35 years. We provide a full dichotomy for the Steiner Tree column by proving that the problem is NP-complete when restricted to Undirected Path graphs. We revise Johnson's summary table according to…

稀疏列联表统计显著性检验中的SAT抽样

SAT-sampling for statistical significance testing in sparse contingency tables

本文提出基于SAT的列联表条件检验抽样方法，将纤维编码为布尔电路，并结合混合MCMC方案，在稀疏及结构零场景下提供可靠的条件p值，优于传统马尔可夫基方法。

Markov Bases for Typical Block Effect Models of Two-way Contingency Tables

Markov basis for statistical model of contingency tables gives a useful tool for performing the conditional test of the model via Markov chain Monte Carlo method. In this paper we derive explicit forms of Markov bases for change point models and block diagonal effect models, which are typical block-wise effect models of two-way contingency tables, and perform conditional tests with some real data sets.

A finiteness theorem for Markov bases of hierarchical models

We show that the complexity of the Markov bases of multidimensional tables stabilizes eventually if a single table dimension is allowed to vary. In particular, if this table dimension is beyond a computable bound, the Markov bases consist of elements of Markov bases of smaller tables. We give an explicit formula for this bound in terms of Graver bases. We also compute these Markov and Graver complexities for all $K \times 2 \times 2 \times 2 $ tables.