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Experimental conformation of the basic principles of length-only discrimination

This study provides experimental evidence supporting the validity and efficiency of the LOD method for length-only discrimination. A test graph with multiple paths is used to demonstrate the need for further research on applying LOD to larger graphs.

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Experimental conformation of the basic principles of length-only discrimination

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  1. Experimental conformation of the basic principles of length-only discrimination Yevgenia Khodor, Julia Khodor, Thomas F. Knight, Jr. Lee Ji Youn

  2. Abstract • Experimental confirmation of the validity of the basic operations of LOD method?? • Test graph consisting of 4 nodes and 3 edges, in which multiple paths are possible!! • Conclude that further work is needed to test the efficiency and practicality of applying LOD methodology to larger graphs!!

  3. Introduction • Adleman • “Generate and Search” approach • error-prone and time-consuming  ineffective • DNA6 • introduction of LOD method for generate and search models of DNA computing • LOD • the scientist is only concerned with the number of base pairs, not their sequence • the encodings of vertices must vary in size in such a way that no summation of an equal number of elements would present the same answer

  4. V3 E23 E12 V1 V2 E24 V4 • Advantage • separation only by size!! • no need in magnetic bead separation • Primitive operations V1-V2-V3 and V1-V2-V4

  5. Algorithm/Implementation • Algorithm for solving HPP 1. Generate all legal paths through the graph 2. Keep only the paths beginning with Vi and Vf 3. Keep only those paths that enter each vertex exactly once 4. If any path remain, return “yes”, otherwise return “no” A band of characteristic size : sum of length of all of the vertices plus (n-1) edges Vertex/Edge Length (in bps) V1 29 V2 12 V3 20 V4 40 E12, E23, E24 63

  6. Method for deriving the length of the vertex encoding • find n different lengths • making a gap between the lengths of the ith and the (i+1)st vertexs be (n+i) • length of the encoding of any path with (i+1) vertexes would be greater than the length of the encoding of any path with i vertexes

  7. Conclusions • The amount of time required to perform a computation is constant, regardless of the size of the graph

  8. Benchmark problem • Maximal clique problem : finding the largest subset of fully interconnected nodes in the given graph • Algorithm : consisting of a series of selection steps containing three parallel selection decisions

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