In this paper, I consider how to implement the basic data structure of LISP programming, the binary tree. I show that, for the compact encoding of LISP trees, three-pointer cells are preferable to the conventional two-pointer ones. The result is one I reported previously, but here the analysis is done more elegantly, using the methods of probabilistic grammars. I also present a detailed implementation of LISP operators for the case in which multi-pointer cells are adopted.

In this paper we consider the problem of optimal wiring of VLSI circuits. The topological placement of the circuit elements (macros) on the chip is assumed to have a special hierarchical structure, i.e., to be a slicing floorplan, represented by a binary (slicing) tree. Instead of the usual objective of minimum wire length, we consider the problem of minimizing the overall area of the wired floorplan. For the case of a single multiterminal net connecting n macros, we obtain a wiring algorithm of complexity O(nd), where d is the depth of the slicing tree. The case of several multiterminal nets is still under investigation.

We present a global wiring algorithm used in a top-down physical design environment, i.e., macros are laid out after global wiring is done, and wires are allowed to pass through macros (the wiring-through model). The floorplan of the chip is in the form of a slicing structure. The algorithm is based on a hierarchical scheme. The final result is obtained through a series of refinement as the problem is recursively decomposed into a set of small-sized problems and then solved efficiently. The worst-case run-time for an arbitrary slicing tree (totally skewed) is O(M /sup 2/ N). When the floorplan is represented by a balanced slicing tree, the run-time of the overall algorithm is O(MN), where M is the number of macros and N the number of nets. The algorithm has been implemented in the C language and is used for chip designs. Experiments on both real and randomly generated designs show that the hierarchical router performs equally well as a flat global router in terms of wire length and wireability handling, but much faster in run-time (at least 10 times for an example with 100 macros and 1000 nets, and the gap being even larger for bigger-size problems).

Statistical measurements of the behavior of LISP programs have shown a marked asymmetry in the distribution of their data structures (binary trees).On the basis of a statistical model for such a distribution, we evaluate the expected storage cost of a representation of binary trees based on the use of k-pointer cells instead of conventional two-pointer ones.We conclude that LISP trees would be more efficiently encoded using three-pointer nodes.

In this paper we discuss a memory allocation problem first introduced by Wolman in [1] (see also [2]). A general solution formula is presented, from which closed form expressions for a few special cases may be easily derived.

No abstract available.

A computer program is described which displays ALGOL arithmetic expressions in two-dimensional form on a line printer or a typesetter.