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**11 - 13**of**13**### PAPER Constructing the Suffix Tree of a Tree with a Large Alphabet

, 1999

"... SUMMARY The problem of constructing the suffix tree of a tree is a generalization of the problem of constructing the suffix tree of a string. It has many applications, such as in minimizing the size of sequential transducers and in tree pattern matching. The best-known algorithm for this problem is ..."

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SUMMARY The problem of constructing the suffix tree of a tree is a generalization of the problem of constructing the suffix tree of a string. It has many applications, such as in minimizing the size of sequential transducers and in tree pattern matching. The best-known algorithm for this problem is Breslauer’s O(n log |Σ|) time algorithm where n is the size of the CS-tree and |Σ | is the alphabet size, which requires O(n log n) time if |Σ | is large. We improve this bound by giving an optimal linear time algorithm for integer alphabets. We also describe a new data structure, the Bsuffix tree, which enables efficient query for patterns of completely balanced k-ary trees from a k-ary tree or forest. We also propose an optimal O(n) algorithm for constructing the Bsuffix tree for integer alphabets. key words: algorithm, suffix tree, common suffix tree, integer alphabet, tree pattern matching 1.

### Practical Amortized Dynamic Indexing

"... The indexing problem is that of preprocessing a (very large) text T so that subsequent searches for patterns P can be accomplished in time O(jP j + tocc), where jP j is the pattern length and tocc is the number of occurrences of the pattern in the text. In the dynamic indexing problem the text ma ..."

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The indexing problem is that of preprocessing a (very large) text T so that subsequent searches for patterns P can be accomplished in time O(jP j + tocc), where jP j is the pattern length and tocc is the number of occurrences of the pattern in the text. In the dynamic indexing problem the text may be changed. We give a practical algorithm that preprocesses the text in time O(n log j\Sigmaj). Subsequently, the total amount of time necessary to do l searches interleaved with k text changes is O(km 2 + lm+ tocc), where m is the length of the maximum sized pattern. We also show how to improve the time to O(km log 2 n + lm + tocc). In the typical case where there are more queries than text changes and the pattern lengths are roughly equal, the time for each pattern query is O(m log 2 n + tocc). 1 Introduction The classical pattern matching problem is that of finding all occurrences of pattern P = p 1 p 2 \Delta \Delta \Delta p m in text T = t 1 t 2 \Delta \Delta \Delta t n ...

### Direct Routing on Trees (Extended Abstract)

- IN PROCEEDINGS OF THE NINTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS (SODA 98
, 1998

"... We consider off-line permutation routing on trees. We are particularly interested in direct tree routing schedules where packets once started move directly towards their destination. The scheduling of start times ascertains that no two packets will use the same edge in the same direction in the same ..."

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We consider off-line permutation routing on trees. We are particularly interested in direct tree routing schedules where packets once started move directly towards their destination. The scheduling of start times ascertains that no two packets will use the same edge in the same direction in the same time step. In O(n log n log log n) time and O(n log n) space, we construct a direct tree routing schedule guaranteed to complete the routing within the general optimum of n - 1 steps. In addition, our scheme guarantees that at most two packets arrive at the same node in the same time step. Furthermore, if the length of the route of a given packet is d and the maximum number of other routes intersecting the route in a single node is k then the packet arrives to its destination within d + k steps.