(ie. polynomial) representation, often using recursive macros. Such compact representations are important since exponential plans are difficult both to use and to understand. We show that these results do not extend to the general case, by proving a number of bounds for compact representations

We consider the problem of representing graphs compactly while supporting queries e#ciently. In particular we describe a data structure for representing n-vertex unlabeled graphs that satisfy an O(n )-separator theorem, c < 1. The structure uses O(n) bits, and supports adjacency and degree

. We prove that -- unless the polynomial hierarchy collapses at the second level -- the size of a purely propositional representation of the circumscription CIRC(T ) of a propositional formula T grows faster than any polynomial as the size of T increases. We then analyze the significance

We consider the problem of efficiently representing sets S of size n from an ordered universe U = {0,...,m−1}. Given any ordered dictionary structure (or comparison-based ordered set structure) D that uses O(n) pointers, we demonstrate a simple blocking technique that pro-duces an ordered set structure supporting the same op-erations in the same time bounds but with O(n log m+nn) bits. This is within a constant factor of the information-theoretic lower bound. We assume the unit cost RAM model with word size Ω(log |U |) and a table of size O(mα log2m) bits, for some constant α> 0. The time bound for our operations contains a factor of 1/α. We present experimental results for the STL (C++ Standard Template Library) implementation of Red-Black trees, and for an implementation of Treaps. We compare the implementations with blocking and without blocking. The blocking variants use a factor of between 1.5 and 10 less space depending on the density of the set. 1

Abstract. The use and study of compact representations of objects is widespread in computer science. AI planning can be viewed as the problem of finding a path in a graph that is implicitly described by a compact representation in a planning language. However, compact representations of the path

(encoding means to provide a compact representation)

Abstract not found

are well-standardized [1,2,3,22], and there are standards for the use and spelling of unit names [2,4], but there are few standards for the representation of units within computing systems. We present a representation which can accommodate unforeseen units, requires minimal agreement among

A new method for the compression of seismic sections based on a surface decomposition strategy is presented. In the decomposition process a function representing the seismic section is rewritten into a sequence of functions whose sum gives an approximation to the original data set. Data compression is obtained by keeping only the coefficients from the components that give a significant contribution to the reconstruction. By significant we shall mean that the distance between the original seismic section and the reconstruction is less than a predefined tolerance in some convenient norm. Experiments show that satisfactory interpretation quality is readily obtained with storage requirements in the range of 1 to 2 bits per sample. This work was supported by Saga Petroleum a.s.

These patterns come from a very simple sequence: 1 2 2 3 3 3 4 4 4 4 5 5 5 5 5 … For example, if this sequence is used for the threading and treadling sequences in a weaving draft with a tabby tie-up, the resulting drawdown is as shown in Figure 1. In the sequence above, each term is replicated according to its value. We know of no good name for this sequence. We have called it the multi sequence in previous articles [1] and the On-Line Encyclopedia of Integer Sequences [2] refers to it as “n appears n times”, which is descriptive but far from elegant. The sequence above is one of a class of sequences obtained by applying term replication functions to bases sequences. For the example above, the base sequence is the positive integers, I + = 1 2 3 4 5 … and the replication function is r(v) = v, where v is the value of the term. If the base sequence is the Fibonacci numbers, F = 1 1 2 3 5 8 …, then this rule yields