
TL;DR
This paper introduces the more realistic problem of Ruler Rolling, where a ruler is folded into a rectangle by folding segments 90 degrees, and provides algorithms to find Pareto-optimal foldings efficiently.
Contribution
It proposes the Ruler Rolling problem, models it with Pareto-optimality, and offers a quadratic-time dynamic programming algorithm for its solution.
Findings
Quadratic-time algorithm for Pareto-optimal Ruler Rolling foldings.
Algorithm remains effective without the last segment length assumption.
Handles objective functions with quadratic complexity efficiently.
Abstract
At CCCG '21 O'Rourke proposed a variant of Hopcroft, Josephs and Whitesides' (1985) NP-complete problem {\sc Ruler Folding}, which he called {\sc Ruler Wrapping} and for which all folds must be 180 degrees in the same direction. Gagie, Saeidi and Sapucaia (2023) noted that if the last straight section of the ruler must be longest, then {\sc Ruler Wrapping} is equivalent to partitioning a string of positive integers into substrings whose sums are increasing such that the last substring sums to at most a given amount. They gave linear-time algorithms for the versions of {\sc Ruler Wrapping} both with and without this assumption. In real life we cannot repeatedly fold a carpenter's ruler 180 degrees in the same direction. In this paper we propose the more realistic problem of {\sc Ruler Rolling}, in which we repeatedly fold the segments 90 degrees in the same direction and thus fold the…
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
TopicsAlgorithms and Data Compression
