Problem NP-complete

Just as there are universal computers that, given a particular input, can simulate any other com-puter, there are NP-complete problems that, with the appropriate input, are effectively equivalent to any NP-hard problem of a given size. For example, Boolean satisfiability -i.e. the problem of determining truth values of the variable s of a Boolean expression so that the expression is true -is known to be an NP-complete problem. See section 12.3.5.2... 

At this point the lower-bounding scheme consists of solving a single machine scheduling problem where for each job i, the release time is the due date is, and the processing time is This nonbottleneck scheme can be further simplified in two steps. First, we can assume that for a/8 =. ., avoiding the need to consider release times of and due dates of, which turns an NP-complete problem, into one solvable in polynomial time. If only one of these were to be relaxed, the schedule can still be foimd in polynomial time by Jackson s rule (Jackson, 1955). Second, we can avoid the computation of completely, by assuming that the maximum is obtained at / = m for all values of i. 

K. G. Murty and S. N. Kabadi. Some NP-complete problems in quadratic and nonlinear programming. Math. Progr., 39 117,1987. 

Once these ontological specifications are created, it is possible to apply reasoning tools to automatically create workflows of services that tackle tasks that require the involvement of multiple services. These are of particular interest, as they offer the possibility of on-the-fly aggregation of services and information in response to a scientist s (potentially complex) query, without the need for workflows to have been predefined. Such reasoning tools already exist, but they require exhaustive search of the Web services space (an NP-complete problem). Techniques and heuristics are being developed in the Semantic Web community to reduce the search spaces and effect efficient searches. We will participate in these efforts while tailoring the searches to cheminformatics. 

The latter is mathematically an NP-complete problem, therefore its size has to be kept minimal. 

The determination of the optimal disassembly sequence is considered a nondeterministic polynomial (NP) complete problem, as the number of alternative sequences increases exponentially with the number of components in the product. Even when including feasibility constraints due to the product stmcture, the size of the problem remains too big for obtaining an optimal solution for complex products (Gungor and Gupta 1998). In order to determine a well-optimized disassembly sequence, three types of methods can be used (Lambert and Gupta 2005) ... 

NP-Complete problem Decision problem (one for which the solution is yes or no ) that has the following property The decision problem can be solved in polynomial deterministic time if all decision problems that can be solved in nondeterministic polynomial time are also solvable in deterministic polynomial time. 

The earliest proposed public key systems were based on NP-complete problems such as the knapsack problem, but these were quickly found to be insecure. Some variants are still considered secure, but are not efficient enough to be practical. The most widely used public key cryptosystems, the RSA and El Gamal systems, are based on number theoretic and algebraic properties. Some newer systems are based on elliptic curves and lattices. Recently, Ronald Cramer and Victor Shoup developed a public key cryptosystem that is both practical and provably secure against adaptive chosen ciphertext attacks, the strongest kind of attack. The RSA system is described in detail below. 

A review of scientific work in artificial chemistry can be found in [7]. Chemical inspired paradigms can be differenced by their parameter representation, which can be explicit or impUdL A DNA based algorithm is applied in [8] to solve the small hitting set problon. This NP-complete problem takes exponential time to solve it and it was demonstrated that when using DNA-based supercomputing, only polynonfial time is needed to solve it. 

Much of the same can be said about running tests to jueld lower bounds for the chromatic number. Even the most immediate one, computing the clique number, is not good, since this is an NP-complete problem as well. The existence of cliques of a fixed size can be decided in poljmomial time, but does not provide a very interesting test. 

The solutions provided until late 80s had not been considered satisfactory to prevent production tardiness. After, probably, the first attempt towards the solution of this NP-complete problem by Pekny and Miller (1991), some approaches using heuristics (by Mussier and Evans 1989), MILP formulation in discrete time (by Kondili 1993 a, b) and continuous time with heuristic (by Cerda et al. 1997) have been proposed. However, one major difficulty with MILP formulations is that the problem size increases exponentially with the number of units/orders. In a most recent work, Berber and... 

---