Combinatorial Algorithms: Enlarged Second Edition (Dover Books on Computer Science) by T. C. Hu & M. T. Shing

Author:T. C. Hu & M. T. Shing [Hu, T. C.]
Language: eng
Format: epub
ISBN: 9780486152943
Publisher: Dover Publications
Published: 2012-04-26T00:00:00+00:00

§5.4 HU-TUCKER ALGORITHM

In the alphabetic tree problem, the order of the leaves V1,V2,...,Vn is given together with their weights w1, w2,..., wn. These sequences are called the node sequence and the weight sequence respectively.

If we combine Vi and Vj, then their father is denoted by Vij and its weight is wij. If Vij and Vk are combined, their father is denoted by Vij,k. In this notion, a single subscript denotes a leaf and double or triple subscript denotes a circular node.

If no confusion should arise, we shall use wi to mean the node Vi with the weight wi. Thus, the phrase “combine (or merge) wi and Wj to form wij" means

“Combine the nodes Vi and Vj with weights wi and Wj, forming a node Vij with weight wij."

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