The zz-matching problem on bipartite graphs

The $z$-matching problem on bipartite graphs is studied with a local algorithm. A $z$-matching ($z \ge 1$) on a bipartite graph is a set of matched edges, in which each vertex of one type is adjacent to at most $1$ matched edge and each vertex of the other type is adjacent to at most $z$ matched edges. The $z$-matching problem on a given bipartite graph concerns finding $z$-matchings with the maximum size. Our approach to this combinatorial optimization are of two folds. From an algorithmic perspective, we adopt a local algorithm as a linear approximate solver to find $z$-matchings on general bipartite graphs, whose basic component is a generalized version of the greedy leaf removal procedure in graph theory. From an analytical perspective, in the case of random bipartite graphs with the same size of two types of vertices, we develop a mean-field theory for the percolation phenomenon underlying the local algorithm, leading to a theoretical estimation of $z$-matching sizes on coreless graphs. We hope that our results can shed light on further study on algorithms and computational complexity of the optimization problem.Comment: 15 pages, 3 figure

OWNERSHIP AND INDUSTRIAL POLLUTION CONTROL: EVIDENCE FROM CHINA

This study explores the differences in pollution control performances of industrial enterprises with various ownerships in China - State owned (SOE), collectively or community owned (COE), privately owned (POE), foreign directly invested (FDI) companies as well as joint ventures. A survey was conducted of approximately 1000 industrial firms in three provinces in China, which collects the detailed firm-level information in the year of 1999. Personal interviews of enterprises managers were also conducted in these samples, and subjective information was collected. Analyses have been performed on the differences in receiving and reacting to environmental regulatory enforcement, community pressure, environmental services, and internal environmental management among different ownerships. The determinants of the industrial pollution emissions in China are identified in the econometrical analyses. The results show that FDI and COE have better environmental performances, while SOEs and the POEs in China are the worst.Environmental Economics and Policy,