## Analog Computer Understanding of Hamiltonian Paths, and a Possible Digitization

**Authors:** Bryce Kim

This paper explores finding existence of undirected hamiltonian paths in a graph using lumped/ideal circuits, specifically low-pass filters. While other alternatives are possible, a first-order RC low-pass filter is chosen to describe the process. The paper proposes a way of obtaining time complexity for counting the number of hamiltonian paths in a graph, and then shows that the time complexity of the circuits is around $O(n \log n)$ where $n$ is the number of vertices in a graph. Because analog computation is often undesirable due to several aspects, a possible digitization scheme is proposed in this paper.

**Comments:** 17 Pages.

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### Submission history

[v1] 2016-07-08 17:30:42

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