Fast algorithms for finding nearest common ancestors
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On finding lowest common ancestors: simplification and parallelization
SIAM Journal on Computing
Randomized algorithms
A computational algorithm for origami design
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On the complexity of protein folding (abstract)
RECOMB '98 Proceedings of the second annual international conference on Computational molecular biology
Folding flat silhouettes and wrapping polyhedral packages: new results in computational origami
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
The complexity of flat origami
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Faster deterministic sorting and priority queues in linear space
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Optimal suffix tree construction with large alphabets
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Efficient randomized pattern-matching algorithms
IBM Journal of Research and Development - Mathematics and computing
Manipulation of Flexible Objects by Geodesic Control
Computer Graphics Forum
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We explore the following problem: given a collection of creases on a piece of paper, each assigned a folding direction of mountain or valley, is there a flat folding by a sequence of simple folds? There are several models of simple folds; the simplest one-layer simple fold rotates a portion of paper about a crease in the paper by ±180°. We first consider the analogous questions in one dimension lower--bending a segment into a flat object--which lead to interesting problems on strings. We develop efficient algorithms for the recognition of simply foldable 1-D crease patterns, and reconstruction of a sequence of simple folds. Indeed, we prove that a 1-D crease pattern is flat-foldable by any means precisely if it is by a sequence of one-layer simple folds. Next we explore simple foldability in two dimensions, and find a surprising contrast: "map" folding and variants are polynomial, but slight generalizations are NP-complete. Specifically, we develop a linear-time algorithm for deciding foldability of an orthogonal crease pattern on a rectangular piece of paper, and prove that it is (weakly) NP-complete to decide foldability of (1) an orthogonal crease pattern on a orthogonal piece of paper, (2) a crease pattern of axis-parallel and diagonal (45-degree) creases on a square piece of paper, and (3) crease patterns without a mountain/valley assignment.