A Polynomial Time Solution to the Clique Problem

Computer-Aided Verification of P/NP Proofs: A Survey and Discussion

“…[4] equal commented [5] and refuted [6] flaws identified [7] equal open letter to the scientific community [8] counterexamples given [9] equal published, but indirectly refuted by [10], implied flaws [11], [12] equal studied and refuted by other scientists [13] flaws identified [14] equal studied in [15] refuted [16] equal patent applied patent granted [17] equal replied in [18] and rebuttal in [19] rebuttal not commented so far [20] equal published without official review [21] not officially verified [22] equal refuted by [6] refuted [23] equal appeared in the Southwest Journal of Pure and Applied Mathematics (discontinued) reviewed [24] equal appeared reviewed [25] equal published reviewed [26] equal Published as a book by WorldScientific reviewed [27] equal published reviewed [28] equal published reviewed [29] equal refuted by [30] refuted [31] not equal underwent a peer review, but was felt not convincing published, but has negative reviews [22] not equal refuted by [32] refuted [33] not equal published in the Journal ISRN Computational Mathematics 2012 ID: 321372, 1-15 not found on the web, only on arxiv [34] not equal refuted by [35] flaws identified [36] not equal refuted by [37] flaws identified [38] not equal retracted (by the author) flaws identified [39] not equal discussed intensively online (by experts) issues identified but left unresolved…”

“…Given that any polynomial-time algorithm to decide any NPcomplete problem would be sufficient to equalize the classes, the natural approach to proving equality is by exhibiting an algorithm to solve any of the known NP-complete or -hard problems. Among the several hundred candidates [60], a few turn out to be particularly popular for this goal: these are the clique or independent set problem [11], [12], [23], [24], [57], [61], [62], satisfiability of logical formulas [4], [7], [9], [14], [17], [20], [27], [62]- [87], [87], [88], Hamiltonian circuits and the traveling salesperson problem [16], [22], [25], [29], [73], [89]- [97], as well as the quadratic assignment problem [98], [99], subset-sum [98], graph isomorphism [68], the polynomial hierarchy and enumerations of perfect matchings [17], diophantine equations [100], maximum cuts [76], constraint satisfaction [83], partition [100], [101], bin packing [28], or fast multiplication of long integers [44] (which is an example of a work concluding equality from a speedup to a computational, not a decision, problem, which is also not asserted as NP-complete). Some work, unfortunately, seemingly disappeared from the internet [20],…”