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- W3130859091 abstract "Chip-firing and rotor-routing are two well-studied examples of Abelian networks. We study the complexity of their respective reachability problems. We show that the rotor-routing reachability problem is decidable in polynomial time, and we give a simple characterization of when a chip-and-rotor configuration is reachable from another one. For chip-firing, it has been known that the reachability problem is in P if we have a class of graphs whose period length is polynomial (for example, Eulerian digraphs). Here we show that in the general case, chip-firing reachability is hard in the sense that if the chip-firing reachability problem were in P for general digraphs, then the polynomial hierarchy would collapse to NP." @default.
- W3130859091 created "2021-03-01" @default.
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- W3130859091 date "2021-02-23" @default.
- W3130859091 modified "2023-09-27" @default.
- W3130859091 title "Rotor-routing reachability is easy, chip-firing reachability is hard" @default.
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