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• W3199375046 abstract "Given a directed multigraph (G=(V,E)), with (|V|=n) nodes and (|E|=m) edges, and an integer z, we are asked to assess whether the number (#ET(G)) of node-distinct Eulerian trails of G is at least z; two trails are called node-distinct if their node sequences are different. This problem has been formalized by Bernardini et al. [ALENEX 2020] as it is the core computational problem in several string processing applications. It can be solved in (mathcal {O}(n^{omega })) arithmetic operations by applying the well-known BEST theorem, where (omega <2.373) denotes the matrix multiplication exponent. The algorithmic challenge is: Can we solve this problem faster for certain values of m and z? Namely, we want to design a combinatorial algorithm for assessing whether (#ET(G) ge z), which does not resort to the BEST theorem and has a predictably bounded cost as a function of m and z. We address this challenge here by providing a combinatorial algorithm requiring (mathcal {O}(mcdot min {z, #ET(G)})) time." @default.
• W3199375046 created "2021-09-27" @default.
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• W3199375046 date "2021-01-01" @default.
• W3199375046 modified "2023-10-12" @default.
• W3199375046 title "Beyond the BEST Theorem: Fast Assessment of Eulerian Trails" @default.
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• W3199375046 doi "https://doi.org/10.1007/978-3-030-86593-1_11" @default.
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