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Christofides algorithm : ウィキペディア英語版 | Christofides algorithm The goal of the Christofides approximation algorithm (named after Nicos Christofides) is to find a solution to the instances of the traveling salesman problem where the edge weights satisfy the triangle inequality. Let be an instance of TSP, i.e. is a complete graph on the set of vertices with weight function assigning a nonnegative real weight to every edge of . == Algorithm == In pseudo-code: # Create a minimum spanning tree of . # Let be the set of vertices with odd degree in and find a perfect matching with minimum weight in the complete graph over the vertices from . # Combine the edges of and to form a multigraph . # Form an Eulerian circuit in (H is Eulerian because it is connected, with only even-degree vertices). # Make the circuit found in previous step Hamiltonian by skipping visited nodes (''shortcutting'').
抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Christofides algorithm」の詳細全文を読む
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