Study on rationality of soccer field dimensions and match time based on the shortest path model and game load density

• 1、Department of Automation, Chongqing University, Chongqing 400044
• 2、College of Mathematics and Statistics, Chongqing University, Chongqing 400044

Abstract：As far as size of soccer field (including length and width) is concerned, this article transformations it as a minimum-cost maximum-flow problem. In order to find an arrangement which helps increase the number of passes to the strikers but guarantees the shortest average distance of players, an algorithm called Successive shortest path and capacity scaling is applied together with Geometry formulas. And a specific method combining former two mathematic methods is structured in the article. The method is based on players' capability and physical condition data, and arrangement on soccer field size obtained by the method is reasonable, because the result makes the game exciting while meeting the minimum physical exertion of players. During experiment, German actual data for 2014 World Cup in Brazil is taken as an example. Then the data are preprocessed to meet the need of process for solving the problem. At last the result compares the actual soccer field size, and they have the high degree of agreement, indicating that the method has a certain credibility. For the analysis of game time, the paper established a race-density evaluation and calculation model for the football game time were evaluated, that the current game time is unreasonable, and gives the reference time.

Keywords： successive shortest path and capacity scaling algorithm minimum-cost maximum-flow problem；geometry formulas game load density