编码与遮蔽:1959-1961年浩然的小说创作

1959年至1961年三年间的经济困难给中国人民留下了深刻的苦难记忆。这个时期浩然的小说创作通过对苦难现实的重新编码,显示出的却是一片阳光灿烂的“艳阳天”。浩然的小说对历史灾难的编码与遮蔽不仅是个人创作的悲剧,而且也是一个时代文学的悲哀。     

Requiring Connectivity in the Set Covering Problem

Given a bipartite graph with bipartition V and W, a cover is a subset C V such that each node of W is adjacent to at least one node in C. The set covering problem seeks a minimum cardinality cover. Set covering has many practical applications. In the context of reserve selection for conservation of species, V is a set of candidate sites from a reserve network, W is the set of species to be protected, and the edges describe which species are represented in each site. Some covers however may assume spatial configurations which are not adequate for conservational purposes. Indeed, for sustainability reasons the fragmentation of existing natural habitats should be avoided, since this is recognized as being disruptive to the species adapted to the habitats. Thus, connectivity appears to be an important issue for protection of biological diversity. We therefore consider along with the bipartite graph, a graph G with node set V, describing the adjacencies of the elements of V, and we look for those covers C V for which the subgraph of G induced by C is connected. We call such covers connected covers. In this paper we introduce and study some valid inequalities for the convex hull of the set of incidence vectors of connected covers.MSC2000: 90C10, 90C57This authors research was financially supported by the Portuguese Foundation for Science and Technology (FCT).This paper is part of this authors Ph.D. research.     

On Disjunctive Cuts for Combinatorial Optimization

In the successful branch-and-cut approach to combinatorial optimization, linear inequalities are used as cutting planes within a branch-and-bound framework. Although researchers often prefer to use facet-inducing inequalities as cutting planes, good computational results have recently been obtained using disjunctive cuts, which are not guaranteed to be facet-inducing in general.A partial explanation for the success of the disjunctive cuts is given in this paper. It is shown that, for six important combinatorial optimization problems (the clique partitioning, max-cut, acyclic subdigraph, linear ordering, asymmetric travelling salesman and set covering problems), certain facet-inducing inequalities can be obtained by simple disjunctive techniques. New polynomial-time separation algorithms are obtained for these inequalities as a by-product.The disjunctive approach is then compared and contrasted with some other general-purpose frameworks for generating cutting planes and some conclusions are made with respect to the potential and limitations of the disjunctive approach.     

多元覆盖阶数和维数的相互关系

将覆盖同余式推广到多元覆盖的情形,给出了多元覆盖的定义,证出了当{〈μi1,…,μin〉(〈mi1,…,min〉)}k i=1为一个n元的覆盖系时.若k≥n,则有k≥n+ψ(min{m n+1,…,mk }),这里ψ表示欧拉函数,mi表示mi1,…,m in的最小公倍数.