In this paper we consider the problem of scheduling on parallel machines with a presence of incompatibilities between jobs. The incompatibility relation can be modeled as a complete multipartite graph in which each ed...
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Binary trees come in two varieties: plane trees, often simply called binary trees, and non-plane trees, in which the order of subtrees does not matter. Nonplane trees find many applications;for example in modeling epi...
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Compression schemes for advanced data structures have become the challenge of today. Information theory has traditionally dealt with conventional data such as text, image, or video. In contrast, most data available to...
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ISBN:
(纸本)9781509018079
Compression schemes for advanced data structures have become the challenge of today. Information theory has traditionally dealt with conventional data such as text, image, or video. In contrast, most data available today is multi-type and context dependent. To meet this challenge, we have recently initiated a systematic study of advanced data structures such as unlabeled graphs [1]. In this paper, we continue this program by considering trees with statistically correlated vertex names. Trees come in many forms, but here we deal with binary plane trees (where order of subtrees matters) and their non-plane version. Furthermore, we assume that each symbol of a vertex name depends in a Markovian sense on the corresponding symbol of the parent vertex name. We first evaluate the entropy for both types of trees. Then we propose for known sources two compression schemes COMPRESSPTREE for plane trees with correlated names, and COMPRESSNPTREE for non-plane trees. We show that these schemes achieve the lower bound within two bits.
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