This is analogous to a graph coloring problem on a graph with weighted edges where the weight represents the length of the string and you are coloring the lowest weight paths through the graph.
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hmm I’ll need to wrap my mind around that
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You could use many force directed algorithms with certain stiffness params and inspect the spring/gravity forces as you pull?
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As a graph theory problem it smells ill-posed. Other have suggested simulation which should get the job done.
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I don’t think that problem is meaningful with graph theory, even with weighted edges.
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If “pull outward” is all leaf nodes in same direction, can probably do it by modifying Floyd–Warshall or Dijkstra alg for shortest path.
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Good question. Doable with finite elements in three-dimensions. Not sure about higher dimensions.
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Graph theory is topological: relations matter but absolute distances (as projected in some visualization of a graph) are meaningless. The concepts of "taut/slack" assume some notion of "equilibrium length" from which tautness or slackness is measured: an absolute distance.
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If you "embed" your topological graph structure into a "metric space" such as 3D-Euclidean space you can then make statements about absolute distances -> definite equilibrium lengths -> make a "Hooke's Law" type assumption to define "taut/slack" as difference from equilibrium.
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