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Using an algebra of paths we present abstract algebraic derivations for two problem classes concerning graphs, viz. layer oriented traversal and computing sets of Hamiltonian paths. In the first case, we are even able to abstract to the very general setting of Kleene algebras. Applications include reachability and a short path problem as well as topological sorting, cycle detection and finding maximum cardinality matchings.
We illustrate the use of formal languages and relations in compact formal derivations of some graph algorithms.
Using an algebra of paths we present abstract algebraic derivations for two problem classes concerning graphs, viz. layer oriented traversal and computing sets of Hamiltonian paths. In the first case, we are even able to abstract to the very general setting of Kleene algebras. Applications include reachability and a shortest path problem as well as topological sorting and finding maximum cardinality matchings.
