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Caching is a promising solution to satisfy the ever increasing demands for the multi-media traffics. In caching networks, coded caching is a recently proposed technique that achieves significant performance gains over the uncoded caching schemes. However, to implement the coded caching schemes, each file has to be split into F packets, which usually increases exponentially with the number of users K. Thus, designing caching schemes that decrease the order of F is meaningful for practical implementations. In this paper, by reviewing the Ali-Niesen caching scheme, the placement delivery array (PDA) design problem is firstly formulated to characterize the placement issue and the delivery issue with a single array. Moreover, we show that, through designing appropriate PDA, new centralized coded caching schemes can be discovered. Secondly, it is shown that the Ali-Niesen scheme corresponds to a special class of PDA, which realizes the best coding gain with the least F . Thirdly, we present a new construction of PDA for the centralized caching system, wherein the cache size of each user M (identical cache size is assumed at all users) and the number of files N satisfies M/N = 1/q or (q − 1)/q (q is an integer such that q ≥ 2). The new construction can decrease the required F from the order O e

Abstract-The technique of coded caching proposed by Madddah-Ali and Niesen is a promising approach to alleviate the load of networks during busy times. Recently, placement delivery array (PDA) was presented to characterize both the placement and delivery phase in a single array for the centralized coded caching algorithm. In this paper, we interpret PDA from a new perspective, i.e., the strong edge coloring of bipartite graph. We prove that, a PDA is equivalent to a strong edge colored bipartite graph. Thus, we can construct a class of PDAs from existing structures in bipartite graphs. The class includes the scheme proposed by Maddah-Ali et al. and a more general class of PDAs proposed by Shangguan et al. as special cases. Moreover, it is capable of generating a lot of PDAs with flexible tradeoff between the sub-packet level and load.

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BackgroundOrange-spotted grouper, Epinephelus coioides, is one of the most valuable fish species in China. Commercial production of orange-spotted grouper could be increased by developing higher growth rates and improving commercially important traits. Information on genetic markers associated with quantitative trait loci (QTL) can be used in breeding programs to identify and select individuals carrying desired traits. A high-density genetic linkage map is the basis for QTL study, and multiplexed shotgun genotyping (MSG) facilitates the development of single nucleotide polymorphisms (SNPs) and genotyping. In this study, the first high-density genetic linkage maps for groupers were generated on the basis of the MSG method.ResultsThe sex-averaged map contained a total of 4,608 SNPs, which spanned 1581.7 cM, with a mean distance between SNPs of 0.34 cM. The 4,608 SNPs were located in 2,849 unique locations on the linkage map, with an average inter-location space at 0.56 cM. There were 2,516 SNPs on the female map, and the number of unique locus was 1,902. However, the male map contained more numbers of SNP (2,939) and unique locations (2,005). The total length of the female and male maps was 1,370.9 and 1,335.5 cM, respectively.ConclusionsThe high-resolution genetic linkage maps will be very useful for QTL analyses and marker-assisted selection (MAS) for economically important traits in molecular breeding of the orange-spotted grouper.

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