Spatial codes and the hardness of string folding problems

Ashwin Nayak*, Alistair Sinclair, Uri Zwick

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review


We present the first proof of NP-hardness (under randomized polynomial time reductions) for string folding problems over a finite alphabet. All previous such intractability results have required an unbounded alphabet size. These problems correspond to the protein folding problem in variants of the hydrophobic-hydrophilic (or HP) model with a fixed number of monomer types. Our proof also establishes the MAX SNP-hardness of the problem (again under randomized polynomial time reductions). This means that obtaining even an approximate solution to the protein folding problem, to within some fixed constant, is NP-hard. Our results are based on a general technique for replacing unbounded alphabets by finite alphabets in reductions for string folding problems. This technique has two novel aspects. The first is the essential use of the approximation hardness of the source problem in the reduction, even for the proof of NP-hardness. The second is the concept of spatial codes, a variant of classical error-correcting codes in which different codewords are required to have large `distance' from one another even when they are arbitrarily embedded in three-dimensional space.

Original languageEnglish
Number of pages10
StatePublished - 1998
Externally publishedYes
EventProceedings of the 1998 9th Annual ACM SIAM Symposium on Discrete Algorithms - San Francisco, CA, USA
Duration: 25 Jan 199827 Jan 1998


ConferenceProceedings of the 1998 9th Annual ACM SIAM Symposium on Discrete Algorithms
CitySan Francisco, CA, USA


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