An exact algorithm for the maximum clique problem

Carraghan, Randy; Pardalos, Pãnos M.

doi:10.1016/0167-6377(90)90057-c

Cited by 434 publications

(292 citation statements)

References 6 publications

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“…We used the relatively simple algorithm described in [22] for finding a maximum clique, and this is the most timeconsuming part of the search procedure.…”

Section: Methodsmentioning

confidence: 99%

Quantum-error-correcting codes using qudit graph states

Looi

Gheorghiu

et al. 2008

Phys. Rev. A

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Graph states are generalized from qubits to collections of n qudits of arbitrary dimension D, and simple graphical methods are used to construct both additive and nonadditive, as well as degenerate and nondegenerate, quantum error correcting codes. Codes of distance 2 saturating the quantum Singleton bound for arbitrarily large n and D are constructed using simple graphs, except when n is odd and D is even. Computer searches have produced a number of codes with distances 3 and 4, some previously known and some new. The concept of a stabilizer is extended to general D, and shown to provide a dual representation of an additive graph code.

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“…We used the relatively simple algorithm described in [22] for finding a maximum clique, and this is the most timeconsuming part of the search procedure.…”

Section: Methodsmentioning

confidence: 99%

Quantum-error-correcting codes using qudit graph states

Looi

Gheorghiu

et al. 2008

Phys. Rev. A

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“…We can not only solve the maximumembedded RHS problem as a set packing problem but can do the reverse as well. Given an m n set packing problem (2), consider the clause set, None of the x j 's can be negatively scaled in the maximum embedded RHS of (3). Clearly, at most one can be negatively scaled, and if one is, y 1 and y 2 must be deleted.…”

Section: Finding a Maximum Embedded Rhsmentioning

confidence: 99%

Detecting embedded Horn structure in propositional logic

Chandru

Hooker

1992

Information Processing Letters

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“…Most of these require a worst-case complexity which is exponential, but in practice, they may do well for many classes of graphs. Some of these algorithms may be found in [4], [6], [7], [11], [12], [15], [18], [20], and [24], and a good survey of all algorithms related to this problem may be found in [21]. Several papers provide good heuristics for the problem, which are typically faster than exact methods, and are often relatively robust in terms of time requirements on different instances.…”

Section: Introductionmentioning

confidence: 99%

Optimized Crossover for the Independent Set Problem

Aggarwal

Orlin

Tai

1997

Operations Research

105

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We propose a knowledge-based crossover mechanism for genetic algorithms that exploits the structure of the solution rather than its coding. More generally, we suggest broad guidelines for constructing the knowledge-based crossover mechanisms. This technique uses an optimized crossover mechanism, in which the one of the two children is constructed in such a way so as to have the best objective function value from the feasible set of children, while the other is constructed so as to maintain the diversity of the search space. We implement our approach on a classical combinatorial problem, called the independent set problem. The resulting genetic algorithm dominates all other genetic algorithms for the problem, and yields one of the best heuristics for the independent set problem in terms of robustness and time performance.

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An exact algorithm for the maximum clique problem

Cited by 434 publications

References 6 publications

Quantum-error-correcting codes using qudit graph states

Quantum-error-correcting codes using qudit graph states

Detecting embedded Horn structure in propositional logic

Optimized Crossover for the Independent Set Problem

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