On a conjecture of Knuth about forward and back arcs
Zipei Nie
TL;DR
This paper proves Knuth's conjecture that in a digraph with a geometric outdegree distribution, the number of forward and back arcs encountered during DFS have identical distributions, using Janson's method.
Contribution
It provides a rigorous proof of Knuth's conjecture on the distributional equality of forward and back arcs in DFS for a specific random digraph model.
Findings
Forward and back arcs are equally distributed in the specified model.
The proof employs Janson's method for probabilistic analysis.
The result confirms a long-standing conjecture by Knuth.
Abstract
Following Janson's method, we prove a conjecture of Knuth: the numbers of forward and back arcs for the depth-first search (DFS) in a digraph with a geometric outdegree distribution have the same distribution.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsBayesian Methods and Mixture Models · Algorithms and Data Compression · Advanced Image and Video Retrieval Techniques