The Traveling-Salesman Problem and Minimum Spanning Trees
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Cites background from "The Traveling-Salesman Problem and ..."
...The Held–Karp (HK) 1-tree lower bound for the symmetric TSP problem is quick and easy to compute [371]....
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2,318 citations
Cites background or methods from "The Traveling-Salesman Problem and ..."
...Held and Karp [27] experimented with primitive-direction ascent in their early work on the traveling salesman problem....
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...It is also worth noting that many other successful Lagrangian relaxations (including Held and Karp [27], [28], Etcheberry [12], Etcheberry, et al....
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...TRAVELING SALESMAN Symmetric Held & Karp [27], [28] Spanning Tree Helbig Hansen and Krarup [26] Spanning Tree Asymmetric Bazarra & Goode [3] Spanning Tree Symmetric Balas & Christofides [1] Perfect 2-Matching Asymmetric Balas & Christofides [I] Assignment...
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...However, the "birth" of the Lagrangian approach as it exists today occurred in 1970 when Held and Karp [27], [28] used a Lagrangian problem based on minimum spanning trees to devise a dramatically successful algorithm for the traveling salesman problem....
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2,248 citations
References
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"The Traveling-Salesman Problem and ..." refers background in this paper
...Whereas the traveling-salesman problem is considered very difficult, the minimum spanning-tree problem can be solved by an algorithm that inspects each edge of K, exactly once[4,12] (see also section 6)....
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5,104 citations
"The Traveling-Salesman Problem and ..." refers background in this paper
...Whereas the traveling-salesman problem is considered very difficult, the minimum spanning-tree problem can be solved by an algorithm that inspects each edge of K, exactly once[4,12] (see also section 6)....
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1,933 citations
1,461 citations
1,073 citations