New Planar P-time Computable Six-Vertex Models and a Complete Complexity Classification

We discover new P-time computable six-vertex models on planar graphs beyond Kasteleyn's algorithm for counting planar perfect matchings. We further prove that there are no more: Together, they exhaust all P-time computable six-vertex models on planar graphs, assuming #P is not P. This leads to the following exact complexity classification: For every parameter setting in ${\mathbb C}$ for the six-vertex model, the partition function is either (1) computable in P-time for every graph, or (2) #P-hard for general graphs but computable in P-time for planar graphs, or (3) #P-hard even for planar graphs. The classification has an explicit criterion. The new P-time cases in (2) provably cannot be subsumed by Kasteleyn's algorithm. They are obtained by a non-local connection to #CSP, defined in terms of a "loop space". This is the first substantive advance toward a planar Holant classification with not necessarily symmetric constraints. We introduce M\"obius transformation on ${\mathbb C}$ as a powerful new tool in hardness proofs for counting problems.Comment: 61 pages, 16 figures. An extended abstract appears in SODA 202

The Complementary Effect of Manufacturing Process Modularity and IS Flexibility on Agility in Manufacturing

In the situation of shortened product life cycles, modular product design enables organizations to adapt to unanticipated changes in their environments. This study extends modular systems theory to manufacturing process design and posits that: (i) firms can design their manufacturing processes for the same product into either an integrated or modularized structure, thereby being agile in dynamic environments, and (ii) the effect of manufacturing process modularity on agility is complemented by information systems (IS) flexibility. Conceptually, this study explains how important the congruence between the IS and manufacturing processes is to achieving agility in manufacturing and seeks to demonstrate how an IS adapts to shape agility. For practice, this study suggests that firms should focus their efforts on both IS flexibility and manufacturing process modularity, as well as their harmonization, in addition to modular product design