In this paper we study the problem of simulating shared memory on the Distributed Memory Machine (DMM). Our approach uses multiple copies of shared memory cells, distributed among the memory modules of the DMM via universal hashing. Thus the main problem is to design strategies that resolve contention at the memory modules. Developing ideas from random graphs and very fast randomized algorithms, we present new simulation techniques that enable us to improve the previously best results exponentially. Particularly, we show that an n-processor CRCW PRAM can be simulated by an n-processor DMM with delay O(log log log n log n), with high probability. Next we show a general technique that can be used to turn these simulations to time-processor optimal ones, in the case of EREW PRAMs to be simulated. We obtain a time-processor optimal simulation of an (n log log log n log n)-processor EREW PRAM on an n-processor DMM with O(log log log n log n) delay. When a CRCW PRAM with (n...

. This paper presents a theoretical study of a model of parallel computations called Parallel Alternating-Direction Access Machine (padam). padam is an abstraction of the multiprocessor computers adena /adenart and a prototype architecture usc/omp. The main feature of padam is the organization of access to the global memory: (1) the memory modules are arranged as a 2-dimensional array, (2) each processor is assigned to a row and a column, (3) the processors switch synchronously between row and column access modes, and can access any of the assigned modules in each mode without conflicts. Since the padam processors have such a restricted access to the partially shared memory, developing tools to enhance flexibility of access to the memory is important. The paper concentrates on these issues. 1 Introduction An important goal in the study of parallel computation is to develop models which are close to real machines but abstract from technical details and provide a vehicle to design and ...

: In this paper we present a (randomized) algorithm for maintaining the biconnected components of a dynamic planar graph of n vertices under deletions of edges. The biconnected components can be maintained under any sequence of edge deletions in a total of O(n log n) time, with high probability. This gives O(logn) amortized time per edge deletion, which improves previous (deterministic) results from [6] due to Giammarresi and Italiano, where O(n log 2 n) amortized time is needed. Our work describes a simplification of the data structures from [6] and uses dynamic perfect hashing to reduce the running time. As in [6], we only need O(n) space. Finally we describe some simply additional operations on the decremental data structure. By aid of them this the data structure is applicable for finding efficiently a \Delta-spanning tree in a biconnected planar graph with a maximum degree 2\Delta \Gamma 2 do to Czumaj and Strothmann [2]. Key Words: dynamic algorithms, graph algorithms, graph c...

The following two computational problems are studied: Duplicate grouping: Assume that n items are given, each of which is labeled by an integer key from the set 0,..., U � 1 4. Store the items in an array of size n such that items with the same key occupy a contiguous segment of the array. Closest pair: Assume that a multiset of n points in the d-dimensional Euclidean space is given, where d � 1 is a fixed integer. Each point is represented as a d-tuple of integers in the range 0,..., U � 14 Ž or of arbitrary real numbers.. Find a closest pair, i.e., a pair of points whose distance is minimal over all such pairs.