We present a randomized and a deterministic data structure for maintaining a dynamic family of sequences under equality tests of pairs of sequences and creations of new sequences by joining or splitting existing sequences. Both data structures support equality tests in O (1) time. The randomized version supports new sequence creations in O(log 2 n) expected time where n is the length of the sequence created. The deterministic solution supports sequence creations in O (log n (log m log* m +log n)) time for the mth operation.

No abstract

A deque with heap order is a linear list of elements with real-valued keys which allows insertions and deletions of elements at both ends of the list. It also allows the ndmin (equivalently ndmax) operation, which returns the element of least (greatest) key, but it does not allow a general deletemin (deletemax) operation. Such a data structure is also called a mindeque (maxdeque). Whereas implementing mindeques in constant time per operation is a solved problem, catenating mindeques in sublogarithmic time has until now remained open. This paper provides an ecient implementation of catenable mindeques, yielding constant amortized time per operation. The important algorithmic technique employed is an idea which is best described as data structural bootstrapping: We abstract mindeques so that their elements represent other mindeques, eecting catenation while preserving heap order. The eciency of the resulting data structure depends upon the complexity of a special case of path compression which we prove requires linear time.

No abstract