In recent years, researchers have been exploring alternative methods to solving Integer Prime Factorization, the decomposition of an integer into its prime factors. This has direct application to cryptanalysis of RSA, as one means of breaking such a cryptosystem requires factorization of a large number that is the product of two prime numbers. This paper applies three different genetic algorithms to solve this issue, utilizing mathematical knowledge concerning distribution of primes to improve the algorithms. The best of the three genetic algorithms has a chromosome that represents m in the equation prime = 6m ± 1, and is able to factor a number of up to 22 decimal digits. This is a significantly larger number than the largest factored by comparable methods in earlier work. This leads to the conclusion that approaches such as genetic algorithms are a promising avenue of research into the problem of integer factorization.

Epidemic contact tracing examines the movement of infection through a population based upon links in a contact network, and weighted networks represent the potential of transfer of the contagion. Graph compression reduces the size of a network by merging groups of nodes into supernodes. This study considers the use of genetic algorithms to select the nodes to be merged, grouping together highly connected sections of the graphs. Examined is a dataset that is extracted from contacts that occurred during several days of the "Infectious: Stay Away" event. The incorporation of weights, to indicate the strength of interactions between individuals, is an important contribution of this work. The demonstrated outcomes are that by including weighted information on the edges, there is more effective detection of highly interacting subgroups when compared to the unweighted version of graphs. These methods not only compress the networks with a low rate of distortion, but also the identification of supernodes in the networks allows for better targeting of interventions by public health upon individuals in such groups. This is crucial because when one member becomes infected, all members of the group are exposed to the contagion.

No abstract

No abstract