Facets of the independent set polytope

Theoretical results pertaining to the independent set polytope P^ISP=conv{x{0,1}ⁿ:Axb} are presented. A conflict hypergraph is constructed based on the set of dependent sets which facilitates the examination of the facial structure of P^ISP. Necessary and sufficient conditions are provided for every nontrivial 0-1 facet-defining inequalities of P^ISP in terms of hypercliques. The relationship of hypercliques and some classes of knapsack facet-defining inequalities are briefly discussed. The notion of lifting is extended to the conflict hypergraph setting to obtain strong valid inequalities, and back-lifting is introduced to strengthen cut coefficients. Preliminary computational results are presented to illustrate the usefulness of the theoretical findings.Mathematics Subject Classification (2000): 90C11, 90C57, 90C35     

Economical Covers with Geometric Applications

A cover of a hypergraph is a collection of edges whose unioncontains all vertices. Let H = (V, E) be a k-uniform, D-regularhypergraph on n vertices, in which no two vertices are containedin more than o(D/e^2k log D) edges as D tends to infinity. Ourresults include the fact that if k = o(log D), then there isa cover of (1 + o(1))n/k edges, extending the known result thatthis holds for fixed k. On the other hand, if k 4 log D thenthere are k-uniform, D-regular hypergraphs on n vertices inwhich no two vertices are contained in more than one edge, andyet the smallest cover has at least (nk) log (k log D)) edges.Several extensions and variants are also obtained, as well asthe following geometric application. The minimum number of linesrequired to separate n random points in the unit square is,almost surely, (n^2/3 / (log n)^1/3). 2000 Mathematical SubjectClassification: 05C65, 05D15, 60D05.     

界面估计问题的有限维数值公式

具体介绍了文献[1]中界面估计问题计算的离散化数值公式。     

超图中的着色问题

本文是近三十年来有关超图中涉及的着色问题的综述。它包含了有关超图着色中的基本结果,临界可着色性,２－可着色性,非２－可着色性以及在超图中与顶点着色、边着色和其它着色相关的极值问题。     

最大k—一致超图

本文刻划直径为ｄ 的最大边数的ｋ－一致超图的结构,推广了Ｏｒｅ 的一个结果     

带运输工具的网络流问题

考虑一个带运输工具的网络流问题。即由一个或者多个供应点向多个需求点通过桌种运输工具（比如货车、轮船等）供应货物的问题,目的是尽可能地降低供应成本．通过一个混和整数规划模型来描述这个问题．并利用拉格朗日松弛结合网络单纯形法得到原问题的一个下界．利用该下界结合试探法得到原问题的可行解．     

4一致(ξ)-超图的最小边数的上界

主要讨论了4一致l-超图的最小边数与最小上色数的关系,给出了上色数为3的4一致l-超图的最小边数的一个上界.     

A Lagrangian Dual Method with Self-Concordant Barriers for Multi-Stage Stochastic Convex Programming

This paper presents an algorithm for solving multi-stage stochastic convex nonlinear programs. The algorithm is based on the Lagrangian dual method which relaxes the nonanticipativity constraints, and the barrier function method which enhances the smoothness of the dual objective function so that the Newton search directions can be used. The algorithm is shown to be of global convergence and of polynomial-time complexity.Mathematics Subject Classification (2000): 90C15, 90C51, 90C06, 90C25, 90C60Research is partially supported by NUS Academic Research Grant R-146-000-006-112     

On Axioms Contituting the Foundation of Hypergraph Theory

Hypergraphs are systems of finite sets, being the most general structures in discrete mathematics and powerful tools in dealing with discrete systems. In general, a branch of mathematics is built on some axioms. Informational scientists introduced the acyclic axiom for hypergraphs. In this paper, we first list several results concerning acyclic hypergraphs, in order to show that Acyclic-Axioms constitute the foundation of acyclic hypergraph theory. Then we give the basic theorem which shows that the Cycle-Axiom covers the Acyclic-Axioms and constitutes the foundation of hypergraph theory.     

Quasi-random hypergraphs

We introduce an equivalence class of varied properties for hypergraphs. Any hypergraph possessing any one of these properties must of necessity possess them all. Since almost all random hypergraphs share these properties, we term these properties quasi-random. With these results, it becomes quite easy to show that many natural explicit constructions result in hypergraphs which imitate random hypergraphs in a variety of ways.