The use of word operations has led to fast algorithms for classic problems such as shortest paths and sorting. Many classic problems in stringology, notably regular expression matching and its variants, as well as edit distance computation, also have transdichotomous algorithms. Some of these algorithms have alphabet restrictions or require a large amount of space. In this paper, we improve on several of the keys results by providing algorithms that improve on known time/space bounds, or algorithms that remove restrictions on the alphabet size. 1

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 \Gamma 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. 1 Introduction In this paper, we consider off-line hot-potato permutation packet routing on trees. We are given a permutation ß of the nodes, and for each node v, we want to send a packet fr...