Ideal matrices and clutters are prevalent in combinatorial optimization, ranging from balanced matrices, of T-joins, to rooted arborescences. Most the known examples ideal nature. In this paper, rendered by recently developed theory cuboids, we provide a different class clutters, one that is geometric The advantage new it allows for infinitely many minimally nonpacking clutters. We characterize...

When estimating how much better a classifier is than random allocation in Q-class ROC analysis, we need to sample from a particular region of the unit hypercube: specifically the region, in the unit hypercube, which lies between the Q− 1 simplex in Q(Q− 1) space and the origin. This report introduces a fast method for randomly sampling this volume, and is compared to rejection sampling of unifo...

We consider the problem of embedding graphs into hypercubes with minimal congestion. Kim and Lai showed that for a given N-vertex graph G and a hypercube it is NP-complete to determine whether G is embeddable in the hypercube with unit congestion, but G can be embedded with unit congestion in a hypercube of dimension 6log N if the maximum degree of a vertex in G is no more than 6log N . Bha...

This paper describes parallel algorithms for the following operations on qua.dtreesboolean operations (union, intersection, complement), collapsing a quadtree, and neighbor finding in an image represented by a quadtree. The architecture assumed in this paper is a. hypercube with one processing element (PE) per hypercube node. We assume that the architecture is SIMD, i.e., all PEs work under the...

A visibility representation of a graph G is an assignment of the vertices of G to geometric objects such that vertices are adjacent if and only if their corresponding objects are “visible” each other, that is, there is an uninterrupted channel, usually axis-aligned, between them. Depending on the objects and definition of visibility used, not all graphs are visibility graphs. In such situations...

Ideal matrices and clutters are prevalent in Combinatorial Optimization, ranging from balanced matrices, clutters of T -joins, to clutters of rooted arborescences. Most of the known examples of ideal clutters are combinatorial in nature. In this paper, rendered by the recently developed theory of cuboids, we provide a different class of ideal clutters, one that is geometric in nature. The advan...

In this paper, we consider polytopes P that are contained in the unit hypercube. We provide conditions on the set of infeasible 0,1 vectors that guarantee that P has a small Chvátal rank. Our conditions are in terms of the subgraph induced by these infeasible 0,1 vertices in the skeleton graph of the unit hypercube. In particular, we show that when this subgraph contains no 4-cycle, the Chvátal...

In this paper, we consider polytopes P that are contained in the unit hypercube. We provide conditions on the set of infeasible 0,1 vectors that guarantee that P has a small Chvátal rank. Our conditions are in terms of the subgraph induced by these infeasible 0,1 vertices in the skeleton graph of the unit hypercube. In particular, we show that when this subgraph contains no 4-cycle, the Chvátal...