Many communication and social networks have power-law link distributions, containing a few nodes that have a very high degree and many with low degree. The high connectivity nodes play the important role of hubs in communication and networking, a fact that can be exploited when designing efficient search algorithms. We introduce a number of local search strategies that utilize high degree nodes in power-law graphs and that have costs scaling sublinearly with the size of the graph. We also demonstrate the utility of these strategies on the GNUTELLA peer-to-peer network.

The evolution of fitness interactions between genes at two major loci is studied where the alleles at a third locus modify the epistatic interaction between the two major loci. The epistasis is defined by a parameter ε and a matrix structure that specifies the nature of the interactions. When ε = 0 the two major loci have additive fitnesses, and when these are symmetric the interaction matrices studied here produce symmetric viabilities of the Wright (1952)-Kimura (1956) form. Two such interaction matrices are studied, for one of which epistasis as measured by |ε| always increases, and for the other it increases when the linkage between the major loci is tight enough and there is initial linkage disequilibrium. Increase of epistasis does not necessarily coincide with increase in equilibrium mean fitness.

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