100 research outputs found
The density and complexity of polynomial cores for intractable sets
Let A be a recursive problem not in P. Lynch has shown that A then has an infinite recursive polynomial complexity core. This is a collection C of instances of A such that every algorithm deciding A needs more than polynomial time almost everywhere on C. We investigate the complexity of recognizing the instances in such a core, and show that every recursive problem A not in P has an infinite core recognizable in subexponential time. We further study how dense the core sets for A can be, under various assumptions about the structure of A. Our main results in this direction are that if P ≠NP, then NP-complete problems have polynomially nonsparse cores recognizable in subexponential time, and that EXPTIME-complete problems have cores of exponential density recognizable in exponential time
Automated rendering of multi-stranded DNA complexes with pseudoknots
We present a general method for rendering representations of multi-stranded
DNA complexes from textual descriptions into 2D diagrams. The complexes can be
arbitrarily pseudoknotted, and if a planar rendering is possible, the method
will determine one in time which is essentially linear in the size of the
textual description. (That is, except for a final stochastic fine-tuning step.)
If a planar rendering is not possible, the method will compute a visually
pleasing approximate rendering in quadratic time. Examples of diagrams produced
by the method are presented in the paper.Comment: 12 pages, 7 figure
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