Compact Data Structures. A Practical Approach by Gonzalo Navarro

By Gonzalo Navarro

Compact info constructions support signify information in decreased house whereas permitting it to be queried, navigated, and operated in compressed shape. they're crucial instruments for successfully dealing with huge quantities of knowledge via exploiting the reminiscence hierarchy. in addition they decrease the assets wanted in allotted deployments and make higher use of the constrained reminiscence in low-end units. the sector has constructed speedily, attaining a degree of adulthood that enables practitioners and researchers in program parts to profit from using compact facts buildings. this primary finished booklet at the subject specializes in the constructions which are so much correct for functional use. Readers will find out how the buildings paintings, tips to decide on the suitable ones for his or her program state of affairs, and the way to enforce them. Researchers and scholars within the zone will locate within the publication a definitive advisor to the cutting-edge in compact facts constructions.

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Huffman, D. A. (1952). A method for the construction of minimum-redundancy codes. Proceedings of the Institute of Electrical and Radio Engineers, 40(9), 1098–1101. Katona, G. O. H. and Nemetz, T. O. H. (1976). Huffman codes and self-information. IEEE Transactions on Information Theory, 22(3), 337–340. Liddell, M. and Moffat, A. (2006). Decoding prefix codes. Software Practice and Experience, 36(15), 1687–1710. Moffat, A. and Turpin, A. (2002). Compression and Coding Algorithms. Springer. , and Bryant, D.

If we interpret going left as the bit 0 and going right as the bit 1, then the path from the root to the leaf of each s ∈ spells out its code C(s). The Huffman tree minimizes the average code length, s∈ Pr(s) · (s). 3 illustrates the Huffman algorithm on the probabilities of 5 2 1 , Pr(b ) = Pr(r ) = 11 , and Pr(c ) = Pr(d ) = 11 . 8: Pr(a ) = 11 Huffman tree on the left assigns the codes C(a ) = 0, C(b ) = 110, C(r ) = 111, C(c ) = 5 2 1 · 1 + 2 × 11 · 3 + 2 × 11 ·3≈ 100, and C(d ) = 101. 040.

Modern Information Theory started with the seminal work of Shannon (1948), presented more in depth in the book by Shannon and Weaver (1949). Gagie (2006) gives more insights on the limits of the kth-order empirical entropy measure. Huffman codes. Huffman (1952) found the well-known algorithm to build an optimal prefix code. Schwartz and Kallick (1964) introduced canonical Huffman codes. Katona bibliography 37 and Nemetz (1976) showed that a symbol with probability p is assigned a Huffman codeword of length at most logφ (1/p) .

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