We consider the effects of parallelizing branch-and-bound algorithms by expanding several live nodes simultaneously. It is shown that it is quite possible for a parallel branch-and-bound algorithm using n 2 processors to take more time than one using n 1 processors even though n 1 < n 2 . Furthermore, it is also possible to achieve speedups that are in excess of the ratio n 2 /n 1 . Experimental results with the 0/1-Knapsack and Traveling Salesperson problems are also presented.

Most successful object recognition systems rely on binary classification, deciding only if an object is present or not, but not providing information on the actual object location. To estimate the object’s location one can take a sliding window approach, but this strongly increases the computational cost, because the classifier or similarity function has to be evaluated over a large set of candidate subwindows. In this paper, we propose a simple yet powerful branch and bound scheme that allows efficient maximization of a large class of quality functions over all possible subimages. It converges to a globally optimal solution typically in linear or even sublinear time, in constrast to the quadratic scaling of exhaustive or sliding window search. We show how our method is applicable to different object detection and image retrieval scenarios. The achieved speedup allows the use of classifiers for localization that formerly were considered too slow for this task, such as SVMs with a spatial pyramid kernel or nearest neighbor classifiers based on the χ²-distance. We demonstrate state-of-the-art localization performance of the resulting systems on the

In discrete optimization problems, we search for an optimal solution among all vectors in a discrete solution space that satisfy a set of constraints, and the search efficiency is of considerable importance since exhaustive search is often impracticable. The method called branch-andbound (noted B&B) is a heuristic tree search algorithm used in this context. Its principle lies in successive decompositions of the original problem in smaller disjoint subproblems until an optimal solution is found, and the search avoids visiting some subproblems which are known not to contain an optimal solution. Given that disjoint subproblems can be decomposed simultaneously and independently, parallel processing has been widely considered as an additional source of improvement in search efficiency, using the set of processors to concurrently decompose several subproblems at each iteration. Parallel B&B is traditionally considered as an irregular parallel algorithm due to the fact that the structure o...

The parallel execution of branch and bound algorithms can result in seemingly unreasonable speedups or slowdowns. Almost never the speedup is equal to the increase in computing power. For synchronous parallel branch and bound, these effects have been studied extensively. For asynchronousparallelizations, only little is known. In this paper, we derive sufficient conditions to guarantee that an asynchronous parallel branch and bound algorithm (with elimination by lower bound tests and dominance) will be at least as fast as its sequential counterpart. The technique used for obtaining the results seems to be more generally applicable. The essential observations are that, under certain conditions, the parallel algorithm will always work on at least one node, that is branchedfrom by the sequential algorithm, and that the parallel algorithm, after elimination of all such nodes, is able to conclude that the optimal solution has been found. Finally, some of the theoretical results are brought i...

This paper analyzes the performances of parallel Branch and Bound algorithm with best-first search strategy by examining various anomalies on the expected speed-up: detrimental, acceleration and detrimental acceleration. Since the best evaluation is not always sufficient to distinguish the best node to choose with best-first search strategy, we define tie breaking rules for cases when nodes have the same value: the fifo, the lifo and the consistent rules. The purpose of the paper is to convey, through bounds of the parallel execution for each tie breaking rule, an understanding of the nature of the anomalies, the range of their impact and a comparison of their efficiency to cope with these anomalies. Sufficient and necessary conditions are given regarding the predisposition for each of the three classes of anomalous behavior. For comparison, we introduce a propriety of proneness to anomaly. In particular, we show that the consistent rule on best-first search Branch and Bound algorithm ...

In this paper we give a classification of parallel branch and bound algorithms and develop a class of asynchronous branch and bound algorithms for execution on an MIMD system. We develop sufficient conditions to prevent the anomalies that can occur due to the parallelism, the asynchronicity or the nondeterminism, from degrading the performance of the algorithm. Such conditions were known already for the synchronous case. It turns out that these conditions are sufficient for asynchronous algorithms as well. We also investigate the consequences of nonhomogeneous processing elements in a parallel computer system. We introduce the notions of perfect parallel time and achieved efficiency to empirically measure the effects of parallelism, because the traditional notions of speedup and efficiency are not capable of fully characterizing the actual execution of an asynchronous parallel algorithm. Finally we present some computational results obtained for the symmetric traveling sa...

In this paper we present an asynchronous branch and bound algorithm for execution on an MIMD system, state sufficient conditions to prevent the parallelism from degrading the performance of this algorithm, and investigate the consequences of having the algorithm executed by nonhomogeneous processing elements. We introduce the notions of perfect parallel time and achieved efficiency to empirically measure the effects of parallelism, because the traditional notions of speedup and processor utilization are not adequate for fully characterizing the actual execution of an asynchronous parallel branch and bound algorithm. Finally we present some computational results obtained for the symmetric traveling salesman problem. 1980 Mathematical Subject Classification: 90C27, 68Q10, 68R05. Key Words & Phrases: parallel computer, MIMD, loosely coupled system, branch and bound, traveling salesman problem, nondeterminism, asynchronicity. Note: This paper will be submitted for publication ...

In this paper we give a classification of parallel branch and bound algorithms and develop a class of asynchronous branch and bound algorithms for execution on an MIMD system. We develop sufficient conditions to prevent the anomalies that can occur due to the parallelism, the asynchronicity or the nondeterminism, from degrading the performance of the algorithm. Such conditions were known already for the synchronous case. It turns out that these conditions are sufficient for asynchronous algorithms as well. We also investigate the consequences of nonhomogeneous processing elements in a parallel computer system. We introduce the notions of perfect parallel time and achieved efficiency to empirically measure the effects of parallelism, because the traditional notions of speedup and efficiency are not capable of fully characterizing the actual execution of an asynchronous parallel algorithm. Finally we present some computational results obtained for the symmetric traveling sa...

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