Similarly, a crcw pram can execute any erew pram algorithm in the same amount of time. Let s be a problem that, on an input of sizen, can be solved on a pram by a parallel algo. The commonly held view is that a pram algorithm should attempt to solve the. Parallel computing pram algorithms semantic scholar.
At first glance, the pram model of computation might not appear to be suitable as a general model for designing efficient parallel algorithms. This is obvious, as the concurrent read facility is not used. Implementing hirschbergs pramalgorithm for connected. The parallel algorithms in this chapter are presented in terms of one popular theoretical model. Abstract we present, in this paper, a detailed translation from algorithms implemented on a standard model of parallel computationthe crew pramto dnabased methods. Pdf efficient time and volume dna simulation of crew. Many though certainly not all of the ideas developed in the context of pram algorithms have proved instrumental in several other models and they are also being used in practical settings of parallel computation. Efficient parallel algorithms for string editing and. Pointer jumping we examine a technique called pointer jumping that.
In computer science, a parallel randomaccess machine pram is a sharedmemory abstract machine. A faster crew pram algorithm for computing cartesian trees. This pram variant allows concurrent reads but not concurrent writes to shared memory locations. A faster distributed singlesource shortest paths algorithm. Among them, aggarwal and park in ap881, and apostolico et al in aalm901 have independently shown that this problem and the more general problem called string editing problem can be solved in ologmlogn time using mnlogm processors on crew pram. In the pram model, there are an unbounded number of processors and a single memory. Parallel random access machines pram is a model, which is considered for most of the parallel algorithms. Optimal parallel two dimensional text searching on a crew. In this paper, we present four erew algorithms for parenthesesmatching that provide new insights into this interesting problem and that are easier to implement compared to the competing algorithms. Our translation is efficient in the following sense. In particular, we provide algorithms for counting the number of points that are directly dominated by each point of a planar point set, and for reporting these point sets.
Separating the power of erew and crew prams with small. Crew versus erew pram algorithm on the crew pram requires olog n time and on3 operations n2 processors perform on ops on the erew pram, the exclusive reads of a ij and b ij values can be satisfied by making n copies of a and b, which takes olog n time with n processors broadcast tree total time is still olog n. X1 odd k 1, k3, k5, km1 and x1 even k2, k4, km similarly. On a crew pram, there is an algorithm that works in time o1 on n processors. If m1, merge two sequence with 1 comparison step 2. Horowitz, sahni and rajasekaran, computer algorithms cs535 parallel algorithms. These algorithms can be simulated in mapreduce using the result of. We introduce a model for narallel computation, called %mob. Unbounded collection of numbered ram processors p 0, p 1, p 2.
In 8 several optimal algorithms for comoarison problems are presented. Parallel algorithms two closely related models of parallel computation. In the same way that the ram is used by sequentialalgorithm designers to model algorithmic performance such as time complexity, the pram is used by parallelalgorithm. Boolean or and and problems on crew and erew prams. Here, multiple processors are attached to a single block of memory.
Pram algorithms parallel random access machine pram. Parallel crew matrix multiplication contents i reminder. Our algorithms are deterministic and designed to run on the concurrent read exclusive write parallel randomaccess machine crew pram. On an erew pram broadcasting can be performed in o log n steps. The processor bounds of all our parallel algorithms can be easily derived by using brents theorem 4. Insights are that efficient mappings of pram algorithms onto gca exist, and that pram and gca optimality criteria differ because the latter takes memory consumption into account. Cartesian tree is a fundamental data structure with many applications in the areas of data structures and string processing. For a boolean function f, let crew cf denote the crew pram complexity of f i. Common all processors writing to same global memory must. A crew pram can execute any erew pram algorithm in the same time. As its name indicates, the pram was intended as the parallelcomputing analogy to the randomaccess machine ram.
The example application serves to explore the considerations sketched above in more detail, and gain more insights into the issues to be considered while implementing a pram algorithm onto a gca. W e presen t a new crew pram algorithm for nding connected comp onen ts. Crcw pram can be simulated by erew pram to run in ot log p time. In this paper, we study the construction of a cartesian tree on a parallel computation model. On a crew pram this requires one parallel step processor i concurrently reads cell 0. The final step takes now also o1 time, those processors with the flag found set can write simultaneously into p 0 s cell tn,pnp. The pram model and algorithms computer science, fsu. There are several other known parallel algorithms for bicc.
Introduction one of the major goals of parallel algorithm design for pram models is to come up with parallel algorithms that are both fast and efficient, i. Crew pram, for any constant o concurrent read exclusive write pram. To implement a pram algorithm on a parallel computer with a network, one must. All our algorithms on a nnode directed hypergraph with fixed degree and diameter can be implemented to ruxi in 0 log% time with mn processors on a crewpram model, where mn is the cost of multiplying two binary matrices. In the erew pram model, different processors may not access the same common memory location when reading or writing. It is an idealized model of a shared memory simd machine. Is there a workoptimal olog2 ntime crew pram convex hull algorithm for odd dimensions greater than 4. An algorithm that runs in t time on the pprocessor priority crcw pram can be simulated by erew pram to run in ot log ptime a concurrent read or write of an pprocessor crcw pram can be implemented on a pprocessor erew pram to execute in olog p time q 1,q p crcw processors, such that q. An algorithm that runs in t time on the pprocessor priority. Although the processors operate in lockstep by executing one instruction per time step, each processor maintains its own state and can therefore execute the program in an arbitrary way according to the control flow.
The pram model and algorithms florida state university. Because they use ramsey theory, both the lower bounds rely crucially on the problems having an extremely large domain relative to the number of inputs at least doubly exponential in the number of inputs. Circuits logic gates andornot connected by wires important measures number of gates depth clock cycles in synchronous circuit pram p processors, each with a ram, local. Oddeven merge using 2m processors algorithm a step 1. Optimal crewpram algorithms for direct dominance problems. Pdf fast connected components algorithms for the erew pram. The above algorithm also shows how an nprocessor erew pram can simulate an nprocessor crew pram with an olgn slowdown. Bitonic sorting on a crew pram coles p arallel merge sort algorithmdescription main principles more details coles p arallel merge sort algorithm implemen. Unbounded collection of shared memory cells m0, m1, m2, each p i has its own unbounded local memory registers and knows. Is there an e cient outputsensitive parallel convex hull algorithm for d 4.
Pram model parallel random access machine is a straightforward and natural generalization of ram. None of previous approximation algorithms for sssp e. Binary tree algorithms for erew pram contents i array minimum i array membership i broadcast i binaryfanin i complete erew array. To appear in the handbook of discrete and computational geometry. The algorithm for merqing was later shown to be implementable on the crew pram 11,3. We would like this message to be read by all n processors of a pram. Abstract we present, in this paper, a detailed translation from algorithms implemented on a standard model of parallel computationthe crew pram to dnabased methods. As we can compute boolean or in o1 time for crcw pram by using following method. Any algorithm designed for the common pram model will execute in the same time.
The parallel computational models we use are the crew pram and erew pram 14. What would be a costoptimal al gorithm to perform the merging. The crewpramis obviously a more powerful model than the erewpram,and the simulation of a crewpram algorithm on an erew. The algorithm uses work on and time olog n for solving. We present a crew pram algorithm that runs in ologn parallel time and has linear work. Parallel random access machine pram pram algorithms p. The fastest way to compute median1d on a crew pram is to use w processors per element of median1d. The algorithms are efficient based on the transitive. One of the earliest crew pram parallel algorithms was presented by eckstein.