In this paper,we consider the generalized prize-collecting Steiner forest problem with submodular penalties(GPCSF-SP problem).In this problem,we are given an undirected connected graph G=(V,E)and a collection of disjo...In this paper,we consider the generalized prize-collecting Steiner forest problem with submodular penalties(GPCSF-SP problem).In this problem,we are given an undirected connected graph G=(V,E)and a collection of disjoint vertex subsets V={V_(1),V_(2),…,V_(l)}.Assume c:E→R_(+)is an edge cost function andπ:2^(V)→R_(+)is a submodular penalty function.The objective of the GPCSF-SP problem is to find an edge subset F such that the total cost including the edge cost in F and the penalty cost of the subcollection S containing these Vi not connected by F is minimized.By using the primal-dual technique,we give a 3-approximation algorithm for this problem.展开更多
Shandong is a culturally powerful province with excellent natural geographical condition and the warm temperate monsoon climate creates abundant benefits to the agricultural development there.In 2009,Shandong administ...Shandong is a culturally powerful province with excellent natural geographical condition and the warm temperate monsoon climate creates abundant benefits to the agricultural development there.In 2009,Shandong administration bureau of Yellow River economic development held the forum on related issues of national new countryside industry office planning to build economic forest base around the Yellow River in Shandong.The primary intention was settled and the construction of Shandong Economic Forest was formally started.Although impressive progress has been achieved in recent years,there also exists potential problems in the construction of economic forest,among which heavy metal pollution and soil acidification are the worst,causing huge damage to the physiological health of the consumers of economic forest.The writer proposes the countermeasures against standardization construction of economic forest.Scientific management is to be adopted to improve the professional skills of the employees in economic forest and brand innovation should be emphasized to quicken the quality certification of the products of economic forest.Besides,standard production demonstration is to be created and promoted in order to boost scale development.Furthermore,mechanism innovation is also to be stressed and forestry specialized cooperation organizations should be largely supported.展开更多
基金This work is supported by the National Natural Science Foundation of China(No.11971146)the Natural Science Foundation of Hebei Province(Nos.A2019205089 and A2019205092)+1 种基金Hebei Province Foundation for Returnees(No.CL201714)Overseas Expertise Introduction Program of Hebei Auspices(No.25305008).
文摘In this paper,we consider the generalized prize-collecting Steiner forest problem with submodular penalties(GPCSF-SP problem).In this problem,we are given an undirected connected graph G=(V,E)and a collection of disjoint vertex subsets V={V_(1),V_(2),…,V_(l)}.Assume c:E→R_(+)is an edge cost function andπ:2^(V)→R_(+)is a submodular penalty function.The objective of the GPCSF-SP problem is to find an edge subset F such that the total cost including the edge cost in F and the penalty cost of the subcollection S containing these Vi not connected by F is minimized.By using the primal-dual technique,we give a 3-approximation algorithm for this problem.
文摘Shandong is a culturally powerful province with excellent natural geographical condition and the warm temperate monsoon climate creates abundant benefits to the agricultural development there.In 2009,Shandong administration bureau of Yellow River economic development held the forum on related issues of national new countryside industry office planning to build economic forest base around the Yellow River in Shandong.The primary intention was settled and the construction of Shandong Economic Forest was formally started.Although impressive progress has been achieved in recent years,there also exists potential problems in the construction of economic forest,among which heavy metal pollution and soil acidification are the worst,causing huge damage to the physiological health of the consumers of economic forest.The writer proposes the countermeasures against standardization construction of economic forest.Scientific management is to be adopted to improve the professional skills of the employees in economic forest and brand innovation should be emphasized to quicken the quality certification of the products of economic forest.Besides,standard production demonstration is to be created and promoted in order to boost scale development.Furthermore,mechanism innovation is also to be stressed and forestry specialized cooperation organizations should be largely supported.
