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Adventures in Algebraic Path Problems

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The classic problem of finding shortest paths in a directed graph can be generalised to finding paths taking path weights in a large class of semirings. This approach has been developed over the last fifty years, with many interesting applications. However, if we try to model some existing Internet routing protocols using semirings we see that the distributivity law [a(b c) = ab ac] is often violated. Since distributivity is vital in semiring theory, we are forced to explore what, if anything, can be accomplished with such “impoverished” algebraic structures.

This talk is part of the Trinity Mathematical Society series.

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