algorithm - Shortest path to connect n points -



algorithm - Shortest path to connect n points -

i have n points , need connect of them minimizing final distance. image above represents algorithm in each node connects nearest 1 final output might of.

i've been searching lot, know pathfinding algos unaware of 1 solves case. found question on math stackexchange reply not providing algorithm - http://math.stackexchange.com/a/581844/156584.

is there algorithm solves problem? otherwise can bruteforce it.

edit: clarification regarding result i'm expecting: each node can connected 2 other nodes, creating continuous path (like taking pen , without ever lifting it, connect nodes minimizing final distance). don't want create cycle (that beingness travelling salesman problem).

ps: question can translated "complete graph n vertices, , wanting take set of edges such graph connected, sum of border weights minimized"

this problem known shortest hamiltonian path problem , np-hard. if number of points small, can utilize backtracking or dynamic programming find optimal solution. if number of points large, can utilize heuristics and/or approximations obtain relatively answer(it not possible find best 1 in case, though).

algorithm graph shortest-path

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