We wanted a scenario where, say, 5 well-placed border points could efficiently represent an area with 5,000 internal points and 10,000 road edges. This would reduce those 10,000 edges to just 5*4/2 = 10 shortcuts for routing through that cluster at a high level – an incredible 1:1000 point ratio and a 30x reduction in edges to consider for the high-level path!
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By WWII, scientists had already begun looking at alternative gelling substances for routine use in bacteriology, but concluded that agar was still better as it is both firmer and easier to handle. Today, some specialized microbiology applications use the colloid carrageenan (extracted from red seaweed Chondrus crispus, or “Irish Moss”), a more transparent and less auto-fluorescent alternative to agar (agar emits its own background fluorescence when excited by light). However, for routine bacteriological use, carrageenan is more difficult to dissolve, requires higher concentrations, can degrade at high temperatures, and forms weaker gels, which may result in puncturing its surface during the plating of cells.