中文摘要：

基于山东省17地市经济发展数据,构建反映城市综合实力的指标体系,利用因子分析法确定城市综合实力得分,以此为基础,建立加权Voronoi图揭示1995~2012年山东省各城市的空间影响范围及演变规律,运用Voronoi树图方法实现了城市多层级嵌套结构的表达,有效反映了城市之间的空间竞争关系,为城市合理布局规划提供了有效论证。

英文摘要：

Based on the economic development data of 17 cities in Shandong province, this paper establishes an evaluation indexes system and uses factor analysis method to calculate the comprehensive power of each city from 1995 to 2012. Based on this, multiplicatively weighted Voronoi diagrams are constructed to reveal urban sphere of influence and changing rules of each city in Shandong province, meanwhile an approach of multiplicatively weighted Voronoi Tree-map is proposed to establish a multi-level nested structure for all cities. It effectively reflects the spatial competition relations between the cities and provides a valid argument for rational layout of urban planning.