Abstract
Motivated by emerging applications for DNA code word design, we consider a generalization of the code word design problem in which an input graph is given which must be labeled with equal length binary strings of minimal length such that the Hamming distance is small between words of adjacent nodes and large between words of non-adjacent nodes. For general graphs we provide algorithms that bound the word length with respect to either the maximum degree of any vertex or the number of edges in either the input graph or its complement. We further provide multiple types of recursive, deterministic algorithms for trees and forests, and provide an improvement for forests that makes use of randomization.
Supported in part by NSF Grant EIA-0112934.
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References
Adleman, L.M.: Molecular computation of solutions to combinatorial problems. Science 266, 1021–1024 (1994)
Aggarwal, G., Cheng, Q., Goldwasser, M.H., Kao, M.-Y., de Espanes, P.M., Schweller, R.T.: Complexities for generalized models of self-assembly. SIAM Journal on Computing 34, 1493–1515 (2005)
Aggarwal, G., Goldwasser, M.H., Kao, M.-Y., Schweller, R.T.: Complexities for generalized models of self-assembly. In: Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms, pp. 880–889 (2004)
Ben-Dor, A., Karp, R., Schwikowski, B., Yakhini, Z.: Universal DNA Tag Systems: A Combinatorial Design Scheme. In: Proceedings of the 4th Annual International Conference on Computational Molecular Biology, pp. 65–75 (2000)
Brenneman, A., Condon, A.E.: Strand Design for Bio-Molecular Computation. Theoretical Computer Science 287(1), 39–58 (2001)
Brenner, S.: Methods for sorting polynucleotides using oligonucleotide tags, U.S. Patent Number 5,604,097 (February 1997)
Brenner, S., Lerner, R.A.: Encoded combinatorial chemistry. In: Proceedings of the National Academy of Sciences of the U.S.A., vol. 89, June 1992, pp. 5381–5383 (1992)
Breuer, M.: Coding vertexes of a graph. IEEE transactions on Information Theory 8, 148–153 (1966)
Breuer, M., Folkman, J.: An unexpected result on coding vertices of a graph. Journal of Mathematical Analysis and Applications 20, 583–600 (1967)
Deaton, R., Garzon, M., Murphy, R.C., Rose, J.A., Franceschetti, D.R., Stevens, J.S.E.: Genetic search of reliable encodings for DNA-based computation. In: Proceedings of the 2nd International Meeting on DNA Based Computers (1996)
Frutos, A.G., Liu, Q., Thiel, A.J., Sanner, A.M.W., Condon, A.E., Smith, L.M., Corn, R.M.: Demonstration of a word design strategy for DNA computing on surfaces. Nucleic Acids Research 25(23), 4748–4757 (1997)
Gaborit, P., King, O.D.: Linear constructions for DNA codes. Theoretical Computer Science 334, 99–113 (2005)
Garzon, M., Deaton, R., Neathery, P., Franceschetti, D.R., Murphy, R.C.: A new metric for DNA computing. In: Proceedings of the 2nd Genetic Programming Conference, pp. 472–478. Morgan Kaufmann, San Francisco (1997)
Gavoille, C., Peleg, D.: Compact and localized distributed data structures. Technical Report RR-1261-01, Laboratoire Bordelais de Recherce en Informatique (2001)
Kao, M.Y., Sanghi, M., Schweller, R.: Randomized fast design of short DNA words. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1275–1286. Springer, Heidelberg (2005)
King, O.D.: Bounds for DNA Codes with Constant GC-content. Electronic Journal of Combinatorics 10(1), #R33, 13 (2003)
Marathe, A., Condon, A., Corn, R.M.: On Combinatorial DNA Word Design. Journal of Computational Biology 8(3), 201–219 (2001)
Shoemaker, D.D., Lashkari, D.A., Morris, D., Mittman, M., Davis, R.W.: Quantitative phenotypic analysis of yeast deletion mutants using a highly parallel molecular bar-coding strategy. Nature Genetics 14(4), 450–456 (1996)
Tsaftaris, S.A.: DNA Computing from a Signal Processing Viewpoint. IEEE Signal Processing Magazine 21, 100–106 (2004)
Tsaftaris, S.A.: How can DNA-Computing be Applied in Digital Signal Processing? IEEE Signal Processing Magazine 21, 57–61 (2004)
Tulpan, D.C., Hoos, H.H.: Hybrid Randomised Neighbourhoods Improve Stochastic Local Search for DNA Code Design. In: Xiang, Y., Chaib-draa, B. (eds.) Canadian AI 2003. LNCS (LNAI), vol. 2671, pp. 418–433. Springer, Heidelberg (2003)
van Lint, J.: Introduction to Coding Theory, 3rd edn. Springer, Heidelberg (1998)
Winfree, E., Liu, F., Wenzler, L., Seeman, N.: Design and self-assembly of two-dimensional DNA crystals. Nature 394, 539–544 (1998)
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Kao, MY., Sanghi, M., Schweller, R. (2006). Flexible Word Design and Graph Labeling. In: Asano, T. (eds) Algorithms and Computation. ISAAC 2006. Lecture Notes in Computer Science, vol 4288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11940128_7
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DOI: https://doi.org/10.1007/11940128_7
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