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- W1715852318 abstract "We study the problem of computing the rank of a divisor on a finite graph, a quantity that arises in the Riemann-Roch theory on a finite graph developed by Baker and Norine (Advances of Mathematics, 215(2): 766-788, 2007). Our work consists of two parts: the first part is an algorithm whose running time is polynomial for a multigraph with a fixed number of vertices. More precisely, our algorithm has running time O(2^{n log n})poly(size(G)), where n+1 is the number of vertices of the graph G. The second part consists of a new proof of the fact that testing if rank of a divisor is non-negative or not is in the complexity class NP intersection co-NP and motivated by this proof and its generalisations, we construct a new graph invariant that we call the critical automorphism group of the graph." @default.
- W1715852318 created "2016-06-24" @default.
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- W1715852318 date "2011-11-30" @default.
- W1715852318 modified "2023-09-27" @default.
- W1715852318 title "The rank of a divisor on a finite graph: geometry and computation" @default.
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