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The 1-median problem on a network asks for a vertex minimizing the sum of the weighted shortest path distances from itself to all other vertices, each associated with a certain positive weight. We allow fornegative weights as well and devise an exact algorithm for the resulting ‘pos/neg-weighted’ problem defined on a cactus. The algorithm visits every(More)
This paper presents a history of a difficult facility layout problem that falls into the category of the Koopmans-Beckmann variant of the Quadratic Assignment Problem (QAP), wherein 30 facilities are to be assigned to 30 locations. The problem arose in 1972 as part of the design of a German university hospital, Klinikum Regensburg. This problem, known as(More)
A highly efficient algorithm (HK) devised by Held and Karp for solving the symmetric traveling-salesman problem was presented at the 7th Mathematical Programming Symposium in 1970 and published in Mathematical Programming in 1971. Its outstanding performance is due to a clever exploitation of the relationship between the traveling-salesman problem and(More)
For a given triangle △ABC, Pierre de Fermat posed around 1640 the problem of finding a point P minimizing the sum s P of the Euclidean distances from P to the vertices A, B, C. Based on geometrical arguments this problem was first solved by Torricelli shortly after, by Simpson in 1750, and by several others. Steeped in modern optimization techniques,(More)