V. Kumar and V.N. Rao, "Load Balancing on the Hypercube Architecture," Proc. Hypercubes, Concurrent Comp., Appli., Mar 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and that are suited to distributed memory machines. In our previous work on parallel A , we developed efficient work distribution strategies [2] that are equally useful for both tree search and graph search problems, and demonstrated their superior performance over other competing methods [4, 5, 6]. We also presented a parallel A algorithm that used a graph formulation to prune all intra processor duplicates, and employed work transfer as a means to partial interprocessor duplicate pruning. An important finding was that the performance improvement obtained using this algorithm employing a ....

....over 10 random samples. Two merits of performance are used: 1) Speedup defined as the ratio T 1 =TP . 2) Isoefficiency function, which is the required rate of growth of T 1 with respect to P , to keep the efficiency fixed at some value, and is a measure of the scalability of the algorithm [6]. In Fig. 3 we plot the speedup for the different parallel A algorithms for N = 24 and for uniformly and normally distributed data. In order to study the advantage of graph search over tree search methods used by other researchers [5, 12] we have also plotted a curve labeled PLA QE Tree. This ....

V. Kumar and V.N. Rao, "Load Balancing on the Hypercube Architecture," Proc. Hypercubes, Concurrent Comp., Appli., Mar 1989.

....log 2 P log 2 b e) Thus T su increases linearly with m and relatively more slowly with b and P . In fact, we see that for the parallel startup phase with constant values of b and m, T su grows only as Theta(logP ) while for a sequential startup phase (b = P , m = 1) used in previous work [4], T su grows as Theta(P ) We first define a few terms that will be useful in our subsequent discussions. By the quality of a node we mean the amount of essential work associated with the node as reflected by its cost (see footnote 1) By uniqueness of nodes across processors we mean the extent ....

....each processor obtains the same number of starting nodes, a good quantity distribution is effected by the startup phase. to neighbors. First we describe two commonly used work distribution strategies for distributed memory machines proposed in previous work, viz. the roundrobin (RR) strategy [4] and the random communication (RC) strategy [2, 3] We then present our new work distribution strategy, which we call quality equalizing (QE) strategy, because of its use of a highly effective scheme for balancing the quality of work between neighbors. 6.1 Previous Strategies: In the ....

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V. Kumar and V.N. Rao, "Load Balancing on the Hypercube Architecture," Proc. Hypercubes, Concurrent Comp., Appli., Mar 1989.

.... 5, 6, 7, 11, 12, 16, 19, 22, 23, 24] However, most of this work has concentrated on parallelization of pure BFS in which sufficient memory is assumed to be available [2, 5, 6, 7, 16, 22, 23, 24] Other related work concerns parallelization of ordinary DFS (i.e. without using lower bound costs) [9, 15, 17, 18, 19, 27, 28, 34]. Very little research in parallel limited memory B B search has been attempted [8, 19, 29, 30, 31] In the next section, we discuss and compare previous sequential and parallel limited memory search methods. Then in Sec. 3, we present a new sequential limited memory search method that can greatly ....

V. Kumar and V.N. Rao, "Load Balancing on the Hypercube Architecture," Proc. Hypercubes, Concurrent Comp., Appli., Mar 1989.

....machines that can be applied to most COP s. In our previous work on parallel A , we developed efficient load balancing strategies [5, 6] that are equally useful for both tree search and graph search problems, and demonstrated their superior performance over other competing methods [1, 11, 13, 17, 25]. In this paper, we develop efficient inter processor duplicate pruning methods, and incorporate them in parallel A algorithms to obtain high speedup over sequential A graph search. In Sec. 2, we first describe A and then present an improved version used in our implementations. Next, in Sec. 3 ....

.... E = T 1 = T 1 T o ) 1= 1 T o =T 1 ) 1= 1 W o =W ) The temporal isoefficiency function Phi T of a parallel algorithm is defined to be the required rate of growth of T 1 with respect to P to keep the efficiency fixed at some value, and is a measure of the scalability of the algorithm [13]. Similarly, the work isoefficiency function Phi W is defined as the required rate of growth of W with respect to P to maintain efficiency at some value. Lower values of Phi W like Theta(P ) and Theta(P Delta log 2 P ) indicate that the algorithm is very scalable, while high values like ....

V. Kumar and V.N. Rao, "Load Balancing on the Hypercube Architecture," Proc. Hypercubes, Concurrent Comp., Appli., Mar 1989.

....have been proposed in past work, they have not adequately addressed the inefficiencies of slow startup and load imbalance. In previous work, a Theta(P ) time sequential startup phase in which a single processor generates the P starting nodes needed for parallel search by all processors was used [12]. Also, no explicit attempts were made to 1 obtain a good initial load balance in prior startup schemes. A number of dynamic load balancing methods for parallel A have also been previously proposed [1, 2, 9, 10, 11, 12, 14, 19, 21, 23] We critically analyze the effectiveness of some ....

....processor generates the P starting nodes needed for parallel search by all processors was used [12] Also, no explicit attempts were made to 1 obtain a good initial load balance in prior startup schemes. A number of dynamic load balancing methods for parallel A have also been previously proposed [1, 2, 9, 10, 11, 12, 14, 19, 21, 23]. We critically analyze the effectiveness of some representative methods in Section 4 and point out their drawbacks. In this paper, we propose a parallel A algorithm with significantly better speedup and scalability than previous algorithms. Our algorithm incorporates (1) a Theta(log P) time ....

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V. Kumar and V.N. Rao, "Load Balancing on the Hypercube Architecture," Proc. Hypercubes, Concurrent Comp., Appli., Mar 1989.

....the isoefficiency function is #(p 3 ) for this parallel system. This is because if the problem size W grows as #(p 3 ) then T o would remain of the same order as W . Isoefficiency analysis has been found to be very useful in characterizing the scalability of a variety of parallel systems [53, 70, 58, 85, 86, 88, 118, 125, 144, 143, 56, 54, 87, 52, 83]. In a single expression, the isoefficiency function captures the characteristics of a parallel algorithm as well as the parallel architecture on which it is implemented. After performing the isoefficiency analysis, we can test the performance of a parallel program on a few processors and then ....

Vipin Kumar and V. N. Rao. Load balancing on the hypercube architecture. In Proceedings of the Fourth Conference on Hypercubes, Concurrent Computers, and Applications, pages 603--608, 1989.

....algorithm and a parallel architecture relates the problem size to the number of processors necessary for an increase in speedup in proportion to the number of processors. Isoefficiency analysis has been found to be very useful in characterizing the scalability of a variety of parallel algorithms [25, 16, 15, 19, 27, 28, 30, 38, 40, 47, 46, 42, 24]. An important feature of isoefficiency analysis is that it succinctly captures the effects of characteristics of the parallel algorithm as well as the parallel architecture on which it is implemented, in a single expression. By performing isoefficiency analysis, one can test the performance of a ....

Vipin Kumar and V. N. Rao. Load balancing on the hypercube architecture. In Proceedings of the Fourth Conference on Hypercubes, Concurrent Computers, and Applications, pages 603--608, 1989.

....schemes and discusses their scalability. Section 7 addresses the effect of variable work transfer cost on overall scalability. Section 8 presents experimental results. Section 9 contains summary of results and suggestions for future work. Some parts of this paper have appeared in [11] and [24]. 2 Definitions and Assumptions In this section, we introduce some assumptions and basic terminology necessary to understand the isoefficiency analysis. 1. Problem size W : the amount of essential computation (i:e: the amount of computation done by the best sequential algorithm) that needs to ....

Vipin Kumar and V. Nageshwara Rao. Load balancing on the hypercube architecture. In Proceedings of the 1989 Conference on Hypercubes, Concurrent Computers and Applications, pages 603--608, 1989.

....larger list of data elements) will have a higher speedup limit. The isoefficiency metric relates the problem size to the number of processors necessary for linear speedup. Isoefficiency analysis has been found to be very useful in characterizing the scalability of a variety of parallel algorithms [15, 22, 16, 8, 14]. An important feature of isoefficiency analysis is that it succinctly captures the behavior of a parallel algorithm in relation to the given parallel architecture. This paper presents two new parallel algorithms QSP1 and QSP2 based on sequential quicksort for sorting data on a mesh multicomputer, ....

Vipin Kumar and V. Nageshwara Rao. Load balancing on the hypercube architecture. In Proceedings of the 1989 Conference on Hypercubes, Concurrent Computers and Applications, pages 603--608, 1989.

.... isoefficiency, which relates the problem size to the number of processors necessary for an increase in speedup in proportion to the number of processors used [14, 15] The isoefficiency analysis has been found to be very useful in characterizing the scalability of a variety of parallel algorithms [15, 21, 22, 16, 9, 13]. By doing isoefficiency analysis, one can test the performance of a parallel program on a small number of processors, and then predict its performance on a larger number of processors. As stated in [21] with this technique we can eliminate (or at least predict) the often reported ....

Vipin Kumar and V. Nageshwara Rao. Load balancing on the hypercube architecture. In Proceedings of the 1989 Conference on Hypercubes, Concurrent Computers and Applications, pages 603--608, 1989.

....size of the problem to increase at the rate necessary to maintain a fixed efficiency, then the parallel system should be considered unscalable from a practical point of view. Isoefficiency analysis has been found to be very useful in characterizing the scalability of a variety of parallel systems [17, 24, 19, 31, 32, 34, 46, 48, 56, 55, 18, 15, 33, 14, 30]. An important feature of isoefficiency analysis is that in a single expression, it succinctly captures the effects of characteristics of a parallel algorithm as well as the parallel architecture on which it is implemented. By performing isoefficiency analysis, one can test the performance of a ....

Vipin Kumar and V. N. Rao. Load balancing on the hypercube architecture. In Proceedings of the Fourth Conference on Hypercubes, Concurrent Computers, and Applications, pages 603--608, 1989.

....26] is one such metric of scalability which is a measure of an algorithm s capability to effectively utilize an increasing number of processors on a parallel architecture. Isoefficiency analysis has been found to be very useful in characterizing the scalability of a variety of parallel systems [19, 15, 24, 25, 28, 35, 36, 39, 38, 14, 26, 13, 22]. An important feature of the isoefficiency function is that it succinctly captures the impact of communication overheads, concurrency, serial bottlenecks, load imbalance, etc. in a single expression. In this paper, we use the isoefficiency metric [24] to analyze the scalability of a number of ....

....as fast as fE (p) to maintain an efficiency E, then fE (p) is defined to be the isoefficiency function of the parallel algorithm architecture combination for efficiency E. Isoefficiency analysis has been found to be very useful in characterizing the scalability of a variety of parallel systems [24, 15, 25, 27, 35, 36, 39, 38, 14, 26, 13, 22]. An important feature of isoefficiency analysis is that in a single expression, it succinctly captures the effects of characteristics of the parallel algorithm as well as the parallel architecture on which it is implemented. By performing isoefficiency analysis, one can test the performance of a ....

Vipin Kumar and V. N. Rao. Load balancing on the hypercube architecture. In Proceedings of the Fourth Conference on Hypercubes, Concurrent Computers, and Applications, pages 603--608, 1989.

.... the scalability of a number of algorithms [9, 14, 17, 21, 23, 24] In particular, it has helped determine optimal load balancing techniques used in tree search based algorithms on various architectures [8, 11, 12, 15] In this paper, we perform scalability analysis, using the Isoefficiency metric [13, 5, 14], of three partitioning algorithms, namely, striped partitioning, binary decomposition, and scattered decomposition. This helps us determine the relative performance of these schemes over a range of processors, and the effect of communication related parameters on the performance of these schemes. ....

Vipin Kumar and V. Nageshwara Rao. Load balancing on the hypercube architecture. In Proceedings of the 1989 Conference on Hypercubes, Concurrent Computers and Applications, pages 603--608, 1989.

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Kumar, V, and V. Rao, "Load balancing on the hypercube architecture," Proceedings of the Fourth Conference on Hypercubes, Concurrent Computers and Applications, Vol 1, pp. 603-608, March 1989

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