TREE COMPRESSION AND OPTIMIZATION WITH APPLICATIONS Dedicated to the memory of Markku Tamminen (1945-1989)

abstractly. Given a tree, the task is to map it as compactly as possible to memory, which is seen as a string of bits, a set of memory locations (words), or a set of memory blocks (pages). The range of the mapping depends on the application in question. In traditional tree compression the only operations performed are encoding of a tree to a bit string and decoding the bit string back to a tree. The benifits gained through data compression of large-to-very-large trees are obvious since compression reduces storage and data transfer requirements. On the other hand, there are some severe disadvantages of tree compression. Above all, compression makes all the normal tree operations (children, parent, search, delete, insert, etc.) more expensive. In most compression methods there is no other way to perform these operations other than to decode the compressed tree, carry out the operation, and encode the tree again! In the tree optimization problem , a term adopted from the work of Jacobson [4], the task is to maintain the functionality of a tree in the compressed form. That is, we want to perform some tree operations as efficiently as done in the uncompressed case (where an operation is a simple matter of pointer manipulation). We are mainly concerned with applications where the trees are manipulated in the internal memory of a computer. So, the mappings are to bit strings or memory words only. For applications concerning external memories, see for example [5,6]. The compression and optimization of trees is usually performed in two phases: the compression of the structure (