V.J. Rayward-Smith, S.A. Rush, and G.P. McKeown. Efficiency considerations in the implementation of parallel branch-and-bound. Annals of Operations Research, 43:123-- 145, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....through the expansion of many nodes of the search tree in parallel. This expansion introduces a breadth wise behaviour into the tree expansion. This technique combined with a depth first sequential strategy for efficient pruning forms the basis of several concurrent branch and bound algorithms[14, 16, 20, 22]. The distinguishing features of the different algorithms for Branch and Bound problems are how they manage local (node) information, information local to a single processor, and global information. Techniques for this management have been suggested in the literature based on message passing [14, ....

....22] The distinguishing features of the different algorithms for Branch and Bound problems are how they manage local (node) information, information local to a single processor, and global information. Techniques for this management have been suggested in the literature based on message passing [14, 20, 22]. 4 Solution, l=20 Solution, l=25 l=18 l=14 l=12 l=8 l=19 l=22 l=4 l=24 Prune Search l=8 l=16 l=9 l=12 Root Figure 1: A partial expansion of a search tree, showing monotonic parameter increases down the tree and the effect of pruning. 3.2.1 Anomalous Behaviour The exact choice ....

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V.J. Rayward-Smith, S.A. Rush, and G.P. McKeown. Efficiency considerations in the implementation of parallel branch-and-bound. Annals of Operations Research, 43:123-- 145, 1993.

....If it appears to have less work, then a smaller value is used, but no smaller than minScatterProb; if it appears to have more work, it uses a larger value, but no larger than maxScatterProb. 4.2. 2 Subproblem tokens When a subproblem is released, only a small portion of its data, called a token [27, 7], is actually sent to the hub. The subproblem itself may move to a secondary pool, called the server pool, that resides on the worker. A token consists of only the information needed RRR 40 2000 Page 17 to identify a subproblem, locate it in the server pool, and schedule it for execution. On a ....

....the most deserving worker. The message sending the subproblem may not go directly to that worker, however; instead, it goes to the worker that originally released the subproblem. When that worker receives the token, it forwards the necessary subproblem information to the target worker, much as in [7, 8, 10, 27]. This process will be described in more detail in Section 4.4.8. Only one subproblem is dispatched at a time; if a token in the hub pool represents several problems, the hub splits it into two, with one token representing one subproblem, and the Page 18 RRR 40 2000 other any remaining ....

V. J. Rayward-Smith, S. A. Rush, and G. P. McKeown, Efficiency considerations in the implementation of parallel branch and bound, Annals of Operations Research 43 (1993) 123-145.

....by parameterisation, and can study the effect of varying workload by appropriate parameterised models. Simulation also gives greater control over some of the behaviour of the system under study. Some of the tree application (e.g. B B) produces a different search space from one run to another [65]. In simulation such behaviour can easily be controlled by the use of artificial tree which generates the workload in a deterministic manner the same shape, depth, fan out and hence the same total workload. Furthermore, simulation allows unlimited number of factors which affect performance to ....

V.J. Rayward-Smith, S.A. Rush, and G.P. McKeown. Efficiency Considerations in the Implementation of Parallel Branch-and-Bound. Annals of Operations Research, 43:123--145, 1993.

....in a distributed system is not trivial as it involves the execution state of the application, which may spontaneously generate new work, and the state of an underlying data structure. Ring based protocols have been a popular means of detecting termination in this type of system, for example[7,11]. The motivation in this work has been the study of algorithms based on shared abstract data types[5] This abstraction technique allows the details of data management to be effectively removed from application code. A significant issue in the design of such types is how they can be used to ....

V.J. Rayward-Smith, S.A. Rush, and G.P. McKeown. Efficiency considerations in the implementation of parallel branch-and- bound. Annals of Operations Research, 43:123--145, 1993.

....not only the CPU power which is increased. Frequently other resources such as memory, cache, etc. increase linearly with the number of processors. The parallel program may be able to achieve super linear speedup by taking advantage of these additional resources. Some examples are presented in [51, 52] where a 32 processor distributed memory parallel machine (with 128Mb of memory, i.e. 4Mb per processor) is more than 32 times as fast as the corresponding single processor machine (also with 4Mb of memory) One of the main objections to parallel processing is Amdahl s law [53] which states that ....

.... nodes, all of priority, p b c Priority p Priority q p q, bound(b) bound(c) m m m m a; b; c; d; Figure 17: An example of an acceleration anomaly McKeown et al. have recently identified a further type of anomaly in parallel Branch and Bound, which they refer to as efficiency anomalies [119, 51]. These anomalies are due to the fact that a parallel system usually has more memory than a sequential one. This extra storage often allows the processors to reduce the amount of work necessary to perform problem expansions. The expansion of a problem state in a Branch and Bound algorithm might ....

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V. J. Rayward-Smith, S. A. Rush, and G. P. McKeown. Efficiency considerations in the implementation of parallel branch-and-bound. Internal report, University of East Anglia, Norwich, 1991.

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