Small portion of simplified(!) North Atlantic food web
In-the-matrix vs On-the-graph
Small graphs can be represented by vertex and edge diagrams, but that's not practical for large or dense systems like the food web above. The vertex and edge representation makes the complexity of the system clear, but isn't helpful to analyze it. Instead we turn to a representation we saw and used earlier in the course: matrices.
Monday we'll see how to represent a graph using a matrix and how to apply the Minimal Spanning Tree and Shortest Route algorithms to matrix representations of graphs.
And some treats ð§ ðŠ ð°
It's a shame that just as the course winds down we finally have the tools to consider some of the most interesting questions. Wednesday we'll look at a few of them as time allows.
The Traveling Salesman Problem. Euler found a simple answer to the question of whether one can traverse a graph crossing each edge exactly once. A seemingly similarly simple problem is to determine the path of least weight that passes through every vertex exactly once, but no efficient solution has been found ?!
The Rule of 72. What do you do when there isn't an efficient, exact mathematical solution? Use a rule of thumb or heuristic.
Game trees. How do computers keep beating people at games? They build game trees to look into the future and see how it will play out.
End of term tweaks
Because of the holidays the last two assignments are not due on Fridays. Moodle does already knows this, but I'll still point out that:
Assignment 11 is due Wednesday April 8.
Assignment 12 is due Wednesday April 15.
Always under construction â ïļ
I had to do a bunch of moving and renaming of resources on the website to accommodate the short weeks. Please let me know if anything seems out of place, or you find broken links. #goodforyourkarma ð
