The Xerox PARC Dragon is a VLSI research computer that uses several techniques to achieve dense code and fast procedure calls in a system that can support multiple processors on a central high bandwidth memory bus.

Let D be a dynamic set of ordered pairs $[ x,y ]$ over the set $0,1, \cdots ,k - 1$ of integers. Consider the following operations applied to D: (1) Insert (delete) a pair $[ x,y ]$ into (from) D. (2) Given test integers $x0,x1$, and $y1$, among all pairs $[ x,y ]$ in D such that $x0 \leqq x \leqq x1$ and $y \leqq y1$, find a pair whose x is minimal (or maximal). (3) Given test integers $x0$ and $x1$, among all pairs $[ x,y ]$ in D such that $x0 \leqq x \leqq x1$, find a pair whose y is minimal. (4) Given test integers $x0$, $x1$, and $y1$, enumerate those pairs $[x,y ]$ in D such that $x0 \leqq x \leqq x1$ and $y \leqq y1$. Using a new data structure that we call a priority search tree, of which two variants are introduced, operations (1), (2), and (3) can be implemented in $O(\log n)$ time, where n is the cardinality of D. Operation (4) is performed in at most $O(\log n + s)$ time, where s is the number of pairs enumerated. The priority search tree occupies $O(n)$ space. Priority seach tree algorithms can be used effectively as subroutines in diverse applications. With them one can answer questions of intersection or containment in a dynamic set of linear intervals. They can be used in combination with a well-known plane-sweep technique, to implement off-line algorithms for enumerating all intersecting pairs of rectangles. Priority search trees can also be used to implement best-/first-fit storage allocation.

We present a new data structure for maintaining a set of records in a linear list according to their key values. This data structure has the property that we can keep a number of fingers at points of interest in the key space (e.g., the beginning or the end of the list), so that access and modification in the neighborhood of a finger is very efficient.

A new algorithm is presented for constructing auxiliary digital search trees to aid in exact-match substring searching. This algorithm has the same asymptotic running time bound as previously published algorithms, but is more economical in space. Some implementation considerations are discussed, and new work on the modification of these search trees in response to incremental changes in the strings they index (the update problem) is presented.

The structure of the functions computable in time or space bounded by t is investigated for recursive functions t. The t-computable classes are shown to be closed under increasing recursively enumerable unions; as a corollary the primitive recursive functions are shown to equal the t-computable functions for a certain recursive t. Any countable partial order can be isomorphically embedded in the family of t-computable classes partially ordered by set inclusion. For any recursive t, there is a recursive t' which is (approximately) equal to an actual running time such that the t-computable functions equal the t'-computable functions.