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Besides the original idea of having a framework for calculating programs from their specifications, avoiding general recursion is also important from a programming methodology point of view. For instance, Meijer et al. [22] stress in their often cited paper the aspect that using folds in functional languages is truly in the spirit of the structured programming methodology. Similar beliefs, that is, avoiding general recursion and using a fixed set of higher order functions, had been already emphasized before by Backus [1]. The programming languages CPL

Given two rooted, ordered, and labeled trees P and T the tree inclusion problem is to determine if P can be obtained from T by deleting nodes in T. This problem has recently been recognized as an important query primitive in XML databases. Kilpeläinen and Mannila (SIAM J. of Comp. 1995) presented the first polynomial time algorithm using quadratic time and space. Since then several improved results have been obtained for special cases when P and T have a small number of leaves or small depth. However, in the worst case these algorithms still use quadratic time and space. In this paper we present a new approach to the problem which leads to a new algorithm which uses optimal linear space and has subquadratic running time. Our algorithm improves all previous time and space bounds. Most importantly, the space is improved by a linear factor. This will make it possible to query larger XML databases and speed up the query time since more of the computation can be kept in main memory.

We answer a basic data structuring question (for example, raised by Dietz and Raman back in SODA 1991): can van Emde Boas trees be made persistent, without changing their asymptotic query/update time? We present a (partially) persistent data structure that supports predecessor search in a set of integers in {1,..., U} under an arbitrary sequence of n insertions and deletions, with O(log log U) expected query time and expected amortized update time, and O(n) space. The query bound is optimal in U for linear-space structures and improves previous near-O((log log U) 2) methods. The same method solves a fundamental problem from computational geometry: point location in orthogonal planar subdivisions (where edges are vertical or horizontal). We obtain the first static data structure achieving O(log log U) worst-case query time and linear space. This result is again optimal in U for linear-space structures and improves the previous O((log log U) 2) method by de Berg, Snoeyink, and van Kreveld (1992). The same result also holds for higherdimensional subdivisions that are orthogonal binary space partitions, and for certain nonorthogonal planar subdivisions such as triangulations without small angles. Many geometric applications follow, including improved query times for orthogonal range reporting for dimensions ≥ 3 on the RAM. Our key technique is an interesting new van-Emde-Boas–style recursion that alternates between two strategies, both quite simple.

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We present new techniques for the construction of uniquely represented data structures in a RAM, and use them to construct efficient uniquely represented data structures for orthogonal range queries, line intersection tests, point location, and 2-D dynamic convex hull. Uniquely represented data structures represent each logical state with a unique machine state. Such data structures are strongly history-independent. This eliminates the possibility of privacy violations caused by the leakage of information about the historical use of the data structure. Uniquely represented data structures may also simplify the debugging of complex parallel computations, by ensuring that two runs of a program that reach the same logical state reach the same physical state, even if various parallel processes executed in different orders during the two runs. 1

Abstract. We consider a data-structural problem motivated by version control of a hierarchical directory structure in a system like Subversion. The model is that directories and files can be moved and copied between two arbitrary versions in addition to being added or removed in an arbitrary version. Equivalently, we wish to maintain a confluently persistent trie (where internal nodes represent directories, leaves represent files, and edge labels represent path names), subject to copying a subtree between two arbitrary versions, adding a new child to an existing node, and deleting an existing subtree in an arbitrary version. Our first data structure represents an n-node degree- ∆ trie with O(1) “fingers ” in each version while supporting finger movement (navigation) and modifications near the fingers (including subtree copy) in O(lg ∆) time and space per operation. This data structure is essentially a locality-sensitive version of the standard practice—path copying— costing O(d lg ∆) time and space for modification of a node at depth d, which is expensive when performing many deep but nearby updates. Our second data structure supporting finger movement in O(lg ∆) time and no space, while modifications take O(lg n) time and space. This data structure is substantially faster for deep updates, i.e., unbalanced tries. Both of these data structures are functional, which is a stronger property than confluent persistence. Without this stronger property, we show how both data structures can be sped up to support movement in O(lg lg ∆), which is essentially optimal. Along the way, we present a general technique for global rebuilding of fully persistent data structures, which is nontrivial because amortization and persistence do not usually mix. In particular, this technique improves the best previous result for fully persistent arrays and obtains the first efficient fully persistent hash table. 1