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• W2093661914 abstract "Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete). In life sciences, combinatorial optimization problems frequently arise in molecular biology, e.g., genome sequencing; global alignment of multiple genomes; identifying siblings or discovery of dysregulated pathways.In almost all of these problems, there is the need for proving a hypothesis about certain property of an object that can be present only when it adopts some particular admissible structure (an NP-certificate) or be absent (no admissible structure), however, none of the standard approaches can discard the hypothesis when no solution can be found, since none can provide a proof that there is no admissible structure. This article presents an algorithm that introduces a novel type of solution method to efficiently solve the graph 3-coloring problem; an NP-complete problem. The proposed method provides certificates (proofs) in both cases: present or absent, so it is possible to accept or reject the hypothesis on the basis of a rigorous proof. It provides exact solutions and is polynomial-time (i.e., efficient) however parametric. The only requirement is sufficient computational power, which is controlled by the parameter $alphainmathbb{N}$. Nevertheless, here it is proved that the probability of requiring a value of $alpha>k$ to obtain a solution for a random graph decreases exponentially: $P(alpha>k) leq 2^{-(k+1)}$, making tractable almost all problem instances. Thorough experimental analyses were performed. The algorithm was tested on random graphs, planar graphs and 4-regular planar graphs. The obtained experimental results are in accordance with the theoretical expected results." @default.
• W2093661914 created "2016-06-24" @default.
• W2093661914 creator A5054123884 @default.
• W2093661914 date "2011-08-26" @default.
• W2093661914 modified "2023-10-01" @default.
• W2093661914 title "Solving Hard Computational Problems Efficiently: Asymptotic Parametric Complexity 3-Coloring Algorithm" @default.
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• W2093661914 hasPublicationYear "2011" @default.
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