A key difficulty in the design of multi-agent robotic systems is the size and complexity of the space of possible designs. In order to make principled design decisions, an understanding of the many possible system configurations is essential. To this end, we present a taxonomy that classifies multiagent systems according to communication, computational and other capabilities. We survey existing efforts involving multi-agent systems according to their positions in the taxonomy. We also present additional results concerning multi-agent systems, with the dual purposes of illustrating the usefulness of the taxonomy in simplifying discourse about robot collective properties, and also demonstrating that a collective can be demonstrably more powerful than a single unit of the collective.

The all nearest smaller values problem is defined as follows. Let A = (a 1 ; a 2 ; : : : ; an ) be n elements drawn from a totally ordered domain. For each a i , 1 i n, find the two nearest elements in A that are smaller than a i (if such exist): the left nearest smaller element a j (with j ! i) and the right nearest smaller element a k (with k ? i). We give an O(log log n) time optimal parallel algorithm for the problem on a CRCW PRAM. We apply this algorithm to achieve optimal O(log log n) time parallel algorithms for four problems: (i) Triangulating a monotone polygon, (ii) Preprocessing for answering range minimum queries in constant time, (iii) Reconstructing a binary tree from its inorder and either preorder or postorder numberings, (vi) Matching a legal sequence of parentheses. We also show that any optimal CRCW PRAM algorithm for the triangulation problem requires \Omega\Gammauir log n) time. Dept. of Computing, King's College London, The Strand, London WC2R 2LS, England. ...

PRAMs also approximate the situation where communication to and from shared memory is much more expensive than local operations, for example, where each processor is located on a separate chip and access to shared memory is through a combining network. Not surprisingly, abstract PRAMs can be much more powerful than restricted instruction set PRAMs. THEOREM 21.16 Any function of n variables can be computed by an abstract EROW PRAM in O(log n) steps using n= log 2 n processors and n=2 log 2 n shared memory cells. PROOF Each processor begins by reading log 2 n input values and combining them into one large value. The information known by processors are combined in a binary-tree-like fashion. In each round, the remaining processors are grouped into pairs. In each pair, one processor communicates the information it knows about the input to the other processor and then leaves the computation. After dlog 2 ne rounds, one processor knows all n input values. Then this processor computes th...

this paper and supplied many helpful comments. This research was supported in part by NSF grants DCR-85-11713, CCR-86-05353, and CCR-88-14977, and by DARPA contract N00039-84-C-0165.

An optimal O(log log n) time parallel algorithm for string matching on CRCWPRAM is presented. It improves previous results of [G] and [V].

) Alberto Apostolico Purdue University and Universit`a di Padova Dany Breslauer yyz Columbia University Zvi Galil z Columbia University and Tel-Aviv University Summary of results Optimal concurrent-read concurrent-write parallel algorithms for two problems are presented: ffl Finding all the periods of a string. The period of a string can be computed by previous efficient parallel algorithms only if it is shorter than half of the length of the string. Our new algorithm computes all the periods in optimal O(log log n) time, even if they are longer. The algorithm can be used to compute all initial palindromes of a string within the same bounds. ffl Testing if a string is square-free. We present an optimal O(log log n) time algorithm for testing if a string is square-free, improving the previous bound of O(log n) given by Apostolico [1] and Crochemore and Rytter [12]. We show matching lower bounds for the optimal parallel algorithms that solve the problems above on a general alphab...

We study the problem of sorting on a parallel computer with limited communication bandwidth. By using the recently proposed PRAM(m) model, where p processors communicate through a small, globally shared memory consisting of m bits, we focus on the trade-off between the amount of local computation and the amount of interprocessor communication required for parallel sorting algorithms. We prove a lower bound of \Omega\Gamma n log m m ) on the time to sort n numbers in an exclusive-read variant of the PRAM(m) model. We show that Leighton's Columnsort can be used to give an asymptotically matching upper bound in the case where m grows as a fractional power of n. The bounds are of a surprising form, in that they have little dependence on the parameter p. This implies that attempting to distribute the workload across more processors while holding the problem size and the size of the shared memory fixed will not improve the optimal running time of sorting in this model. We also show that bot...

This talk presents the derivation of an\Omega\Gamma/28 log m) lower bound on the number of rounds necessary for finding occurrences of a pattern string P [1::m] in a text string T [1::2m] in parallel using m comparisons in each round. The parallel complexity of the string matching problem using p processors for general alphabets follows. 1. Introduction Better and better parallel algorithms have been designed for string-matching. All are on CRCW-PRAM with the weakest form of simultaneous write conflict resolution: all processors which write into the same memory location must write the same value of 1. The best CREW-PRAM algorithms are those obtained from the CRCW algorithms for a logarithmic loss of efficiency. Optimal algorithms have been designed: O(logm) time in [8, 17] and O(log log m) time in [4]. (An optimal algorithm is one with pt = O(n) where t is the time and p is the number of processors used.) Recently, Vishkin [18] developed an optimal O(log m) time algorithm. Unlike...

All algorithms below are optimal alphabet-independent parallel CRCW PRAM algorithms. In one dimension: Given a pattern string of length m for the string-matching problem, we design an algorithm that computes a deterministic sample of a sufficiently long substring in constant time. This problem used to be a bottleneck in the pattern preprocessing for one- and two-dimensional pattern matching. The best previous time bound was O(log 2 m= log log m). We use this algorithm to obtain the following results. 1. Improving the preprocessing of the constant-time text search algorithm [12] from O(log 2 m= log log m) to O(log log m), which is now best possible. 2. A constant-time deterministic string-matching algorithm in the case that the text length n satisfies n = \Omega\Gamma m 1+ffl ) for a constant ffl ? 0. 3. A simple probabilistic string-matching algorithm that has constant time with high probability for random input. 4. A constant expected time Las-Vegas algorithm for computing t...

We analyze the complexity of simulating a PRAM (parallel random access machine) on a mesh structured distributed memory machine. By utilizing suitable algorithms for randomized hashing, routing in a mesh, and sorting in a mesh, we prove that simulation of a PRAM on p N \Theta p N (or 3 p N \Theta 3 p N \Theta 3 p N ) mesh is possible with O( p N ) (respectively O( 3 p N )) delay with high probability and a relatively small constant. Furthermore, with more sophisticated simulations further speed-ups are achieved; experiments show delays as low as p N + o( p N ) (respectively 3 p N + o( 3 p N )) per N PRAM processors. These simulations compare quite favorably with PRAM simulations on butterfly and hypercube. 1 Introduction PRAM 1 (Parallel Random Access Machine) is an abstract model of computation. It consists of N processors, each of which may have some local memory and registers, and a global shared memory of size m. A step of a PRAM is often seen to consist of...