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- W1483267013 abstract "Valiant (SIAM Journal on Computing 8, pages 410-421) showed that the problem of counting the number of s-t paths in graphs (both in the case of directed graphs and in the case of undirected graphs) is complete for #P under polynomial-time one-Turing reductions (namely, some post-computation is needed to recover the value of a #P-function). Valiant then asked whether the problem of counting the number of self-avoiding walks of length n in the two-dimensional grid is complete for #P1, i.e., the tally-version of #P. This paper offers a partial answer to the question. It is shown that a number of versions of the problem of computing the number of self-avoiding walks in two-dimensional grid graphs (graphs embedded in the two-dimensional grid) is polynomial-time one-Turing complete for #P.This paper also studies the problem of counting the number of self-avoiding walks in graphs embedded in a hypercube. It is shown that a number of versions of the problem is polynomial-time one-Turing complete for #P, where a hypercube graph is specified by its dimension, a list of its nodes, and a list of its edges. By scaling up the completeness result for #P, it is shown that the same variety of problems is polynomial-time one-Turing complete for #EXP, where the post-computation required is right bit-shift by exponentially many bits and a hypercube graph is specified by: its dimension, a boolean circuit that accept its nodes, and one that accepts its edges." @default.
- W1483267013 created "2016-06-24" @default.
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- W1483267013 date "2001-01-01" @default.
- W1483267013 modified "2023-09-27" @default.
- W1483267013 title "The Complexity of Computing the Number of Self-Avoiding Walks in Two-Dimensional Grid Graphs and in Hypercube Graphs" @default.
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- W1483267013 doi "https://doi.org/10.1007/3-540-44683-4_51" @default.
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