An instance of Guan's route inspection problem (black edges and weights) and its optimal solution (doubling the red edges to produce an Eulerianmultigraph)
Guan is known for formulating the route inspection problem.[1] This problem is a generalization of the Euler tour problem, in which the input is an edge-weighted graph and the goal is to find a closed walk of minimum total weight that visits every graph edge at least once. Its applications include transportation planning problems such as planning routes for a fleet of snowplows to plow all the streets of a city, in minimum total time.[2]
Guan worked as a lecturer at Shandong Normal University during the Great Leap Forward of 1958–1960, during which Chinese mathematicians were encouraged to work on practical problems. He published his work on the route inspection problem in 1960, and his paper was translated into English in 1962.[1] It attracted the attention of Jack Edmonds, who gave the problem its alternative name, the "Chinese postman problem", in honor of Guan,[3] and proved that this problem can be solved optimally in polynomial time.[1]
One of Guan's later contributions was to prove that, in contrast, the windy postman problem is NP-complete; this is a generalized version of the route inspection problem in which the cost of traversing an edge depends on the direction in which it is traversed.[4]
Kwan, Mei-ko (1960), "奇偶点图上作业法" [Graphic programming using odd or even points], Acta Mathematica Sinica (in Chinese), 10: 263–266, MR0162630. Translated in Chinese Mathematics1, American Mathematical Society, 1962, pp. 273–277.
Guan, Meigu; Zheng, Handing (1983), 线性规划 [Linear Programming] (in Chinese), Shandong Science and Technology Press.
Guan, Meigu (1989), "Graph theory in China", Graph theory and its applications: East and West (Jinan, 1986), Annals of the New York Academy of Sciences, vol. 576, New York: New York Academy of Sciences, pp. 203–218, doi:10.1111/j.1749-6632.1989.tb16400.x, MR1110817, S2CID86165306.
