Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. I. The One-Dimensional Case

We give an algorithm for testing the extremality of minimal valid functions for Gomory and Johnson's infinite group problem that are piecewise linear (possibly discontinuous) with rational breakpoints. This is the first set of necessary and sufficient conditions that can be tested algorithmically for deciding extremality in this important class of minimal valid functions. We also present an extreme function that is a piecewise linear function with some irrational breakpoints, whose extremality follows from a new principle.Comment: 38 pages, 10 figure

A Ricardo Model with Economies of Scale

trade ; production ; tariffs ; commodities

A Ricardo Model with Economies of Scale

economic theory ; economic models

Toward a Theory of Industrial Policy-Retainable Industries

economic theory ; production

A Country's Maximal Gains from Trade and Conflicting National Interests

This paper shows that there are gains from trade that a country can capture from a partly developed trading partner that strongly exceed the gains it can obtain by trading with a fully developed one. We will also show that these gains are beneficial to one country only, they always come at the expense of the trading partner. We will also discuss more generally the circumstances under which improvements in productivity in a trading partner are beneficial to the home country.TRADE ; MODELS ; ECONOMIC EQUILIBRIUM

Scale Economies, Regions of Multiple Trade Equilibria, and the Gains from Acquisition of Industries

economic equilibrium ; economic models ; market ; industry

Linear Trade-Model Equilibrium regions, Productivity, and Conflicting National Interests.

This paper examines the many equlibria that arises in a family of linear models in which the production parameters vary among models.LINEAR MODELS;ECONOMIC EQUILIBRIUM;PRODUCTIVITY

Hierarchies of Predominantly Connected Communities

We consider communities whose vertices are predominantly connected, i.e., the vertices in each community are stronger connected to other community members of the same community than to vertices outside the community. Flake et al. introduced a hierarchical clustering algorithm that finds such predominantly connected communities of different coarseness depending on an input parameter. We present a simple and efficient method for constructing a clustering hierarchy according to Flake et al. that supersedes the necessity of choosing feasible parameter values and guarantees the completeness of the resulting hierarchy, i.e., the hierarchy contains all clusterings that can be constructed by the original algorithm for any parameter value. However, predominantly connected communities are not organized in a single hierarchy. Thus, we develop a framework that, after precomputing at most $2(n-1)$ maximum flows, admits a linear time construction of a clustering \C(S) of predominantly connected communities that contains a given community $S$ and is maximum in the sense that any further clustering of predominantly connected communities that also contains $S$ is hierarchically nested in \C(S). We further generalize this construction yielding a clustering with similar properties for $k$ given communities in $O(kn)$ time. This admits the analysis of a network's structure with respect to various communities in different hierarchies.Comment: to appear (WADS 2013

Reverse Chv\'atal-Gomory rank

We introduce the reverse Chv\'atal-Gomory rank r*(P) of an integral polyhedron P, defined as the supremum of the Chv\'atal-Gomory ranks of all rational polyhedra whose integer hull is P. A well-known example in dimension two shows that there exist integral polytopes P with r*(P) equal to infinity. We provide a geometric characterization of polyhedra with this property in general dimension, and investigate upper bounds on r*(P) when this value is finite.Comment: 21 pages, 4 figure