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...n optimization problem (the workers are independent). In order to balance the subproblems that have to be solved some works have been done about the decomposition of the search tree based on its size =-=[8,3,7]-=-. However, the tree size is only approximated and is not strictly correlated with the resolution time. Thus, as mentioned by Bordeaux et al. [1], it is quite difficult to ensure that each worker will ...

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...ointing is necessary. However, as we pointed out previously, writing descriptions of all open nodes to disk is likely to be excessive. One solution is to write only the roots of subtrees, as stored by the load coordinator. In this case, some work is lost, but not all. The effectiveness of this depends very much on the instance. The biggest challenge is to decide which instances fall into the category of ILPs for which this type of computing is appropriate. So far, it has proven difficult to estimate the number of B&B nodes that will be needed to solve an instance early in the solution process [19, 40]. It remains very unclear how many more instances could be solved if 10, 100, or 1000 times the number of nodes could be evaluated. The instances that could likely profit the most from additional node evaluations are those instances for which the LPs are hard to solve and the number of nodes processed per second is the limiting factor. Here, using a million cores clearly offers a viable approach. 7 Solution of Very Large ILPs We have assumed thus far that the size of an instance is small enough to fit into the memory of a single PE, which limits us a priori to instances of a certain maximum si...

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...lve some of the problems which have seemed to be intractable in the past. 2 MIPLIB 2003 MIPLIB 2003 is a standard and widely used benchmark to compare the performance of various MIP algorithms (e.g., =-=[2, 3, 7, 10, 11, 12, 15, 16, 19, 20, 21, 22, 23, 24, 25, 27, 35]-=-). This library is publicly available athttp://miplib.zib.de ([5]) and consists of 60 (minimization)sPage 2 RRR 2–2007 problems, each one having special characteristics, and described in more detail i...

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...ating search complexity goes back to [10] and more recently [9], which predict the size of general backtrack trees through random probing. Similar schemes were devised for Branch and Bound algorithms =-=[2]-=-, where search is run for a limited time and the partially explored tree is extrapolated. These approaches typically require a substantial amount of probing, which is prohibitively expensive in our se...

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...the performance of search go back to [9] and more recently [10], which predict the size of general backtrack trees through random probing. Similar schemes were devised for Branch and Bound algorithms =-=[11]-=-: B&B is run for a limited time and the partially explored tree is extrapolated. Our method, on the other hand, is not based on sampling or probing but only uses parameters available a priori and info...

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... learning as well.September 21, 2010 0:4 WSPC - Proceedings Trim Size: 11in x 8.5in psb11-parallel-haplotypes-final Using Equation 3, our prediction for ¯ D(n) is: ¯D ∗ (n) = (U(n)−L(n))·h(n)α inc ∗ =-=(4)-=- Predicting N(n) for a New Subproblem P(n) : Given the estimates b ∗ and inc ∗ as derived above, we will predict the number of nodes N(n) generated within P(n) as: N ∗ (n) = b ∗ ¯ D ∗ (n) (5) The assu...

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...mating search complexity goes back to [8] and more recently [6], which predict the size of general backtrack trees through random probing. Similar schemes were devised for Branch and Bound algorithms =-=[2]-=-, where search is run for a limited time and the partially explored tree is extrapolated. Our approach differs by sampling and learning entirely during preprocessing, allowing very fast repeated estim...