Michael J. Quinn, "Analysis and Implementation of Branch-and-Bound Algorithms on a Hypercube Multicomputer", IEEE Transactions on Computers, vol. C-39, Pages 384-387, no. 3, March, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of processors used. Consequently, since AABBs are very fast to test for overlap, we only got very limited speedup 30 with 4 processors. For OBBs, however, the speedup peaks at 3.2 as can be seen in Figure 1. d) 6 Related Work and Discussion Several older parallel branch and bound techniques [2, 5, 7, 9, 10, 19] and depthfirst search algorithms like backtracking [11 13] seem at a first glance to be applicable to the applications we have at hand. Our results indicate, however, that the load distribution strategies in these algorithms do not apply very well to tree traversals found in VFC and collision ....

Michael J. Quinn, "Analysis and Implementation of Branch-and-Bound Algorithms on a Hypercube Multicomputer", IEEE Transactions on Computers, vol. C-39, Pages 384-387, no. 3, March, 1990.

....and bound algorithms in parallel processing. In 1984, T.H.Lai and S.Sahni [5] showed the anomalous behavior of parallel branch and bound algorithms. Recently, after putting parallel processing to practical use, results from several implementations on branch and bound algorithms have been presented [2, 6, 7, 9, 10, 12, 14, 15, 16]. The parallelized algorithms (generally called parallel branch and bound algorithms) can be designed in such a way, that there is no interaction between the subproblem currently being solved in parallel and the rest of the existing subproblems (subproblems are generated during the enumeration ....

M.J.Quinn, "Analysis and Implementation of Branch-and-Bound Algorithms on a Hypercube Multicomputer," IEEE Transactions on Computers, 39(3) (1990) 384-387.

....power of the hybrid selection rule in the real world cases. It is known that the number of subproblems visited in a sequential branch and bound algorithm is minimized when the best bound first selection is applied. Therefore, implementations have often been applied to the best bound selection rule[7, 8, 11]. However, the idea is based on the assumption that the evaluation of each subproblem takes up the same computing time. Our results showed that the evaluation time varies significantly(see Table 1) in practice. Based on the experimental facts, the advantages of the hybrid selection rule, both in ....

M. J. Quinn. Analysis and implementation of branch-andbound algorithms on a hypercube multicomputer. IEEE Transactions on Computers, 39(3):384--387, 1990.

.... 80s [513] A number of commercial offerings have been made since then, the most enduring of which are the iPSC series from Intel [28] and the nCUBE machines [258, 443, 174] Both provide partitioning as described below. Many hypercube applications are specifically tailored to the topology (e.g. [41, 495, 475]) Therefore if an application is to run on a partition of the machine, that partition must itself be a hypercube, albeit of a smaller dimensionality 4 . It is easy to see that there are many ways in which to satisfy this requirement. For example, all the nodes whose IDs start with the bit 1 ....

M. J. Quinn, "Analysis and implementation of branch-and-bound algorithms on a hypercube multicomputer". IEEE Trans. Comput. 39(3), pp. 384--387, Mar 1990.

....of a particular processor. Search spaces to partition are taken from centralized subspace storage and generated composite subspaces are reinserted. The centralized best solution found so far is updated with discovered superior solutions and inferior search spaces are pruned against it [WaM84] [Qui90]. The distributed approach consists of private subspace storage and a private best solution found so far in the local memory of every processor. Each local partitioning process can distribute generated composite subspaces to other processors by asynchronous communication and broadcasts new best ....

....storage and a private best solution found so far in the local memory of every processor. Each local partitioning process can distribute generated composite subspaces to other processors by asynchronous communication and broadcasts new best solutions to all processors [EDH80] JAM88] TrO89] [Qui90]. Two straightforward parallel functional implementations have imitated the imperative approaches without using their asynchronous communication methods, because the fork join model does not permit any direct communication between parallel jobs. Indirect communication has to be committed to ....

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M.J. Quinn, Analysis and Implementation of Branch-and-Bound Algorithms on a Hypercube Multicomputer , IEEE Transactions on Computers, Vol. 39, No. 3, pp. 384--387, March 1990.

....knowledge of attributes of the nodes in this data structure to maintain its efficiency. This atypical nature of the algorithm has focused research on its parallelization on distributed memory multiprocessors in which expensive message passing is the only means of interprocessor communications [1, 8, 13, 15]. It has been commonly assumed that multiprocessors with globally shared memory will provide efficient support for both the irregular and dynamic nature of the data structure, and for the maintenance of global knowledge. This paper suggests otherwise, and presents results which indicate that ....

M. J. Quinn, "Analysis and implementation of branch and bound algorithms on a hypercube multicomputer," IEEE Transactions on Computers, vol. 39, no. 3, pp. 384--387, 1990.

....priorit e par rapport a celles de tous les noeuds en attente dans la file locale de tous les processeurs. Laboratoire PRiSM Strat egie Dynamique Pour l Equilibrage de Charge : Mod ele Multi Control 3 D autres travaux effectu es sur ce mod ele sont ceux de Eckstein [11] Felten [12] et Quinn[28, 29], Luling et Monien dans [23] et Vornberger dans [36] Nous remarquons cependant que les performances peuvent etre d egrad ees a cause du nombre important de sous probl emes non prometteurs (c est a dire ne conduisant pas a l identification de solutions bonnes ou optimales ) qui peuvent etre ....

....d abord, largeur d abord et al. eatoire. S agit il d une ex ecution parall ele ou s equentielle, ces strat egies qui d efinissent des priorit es entre les sous probl emes a traiter ont toujours et e conserv ees. N eanmoins, une pr ef erence a et e donn ee a la strat egie meilleur d abord, Quinn [29], Mans et Roucairol [8] Elle a et e reconnue comme la plus performante en complexit e temporelle. Comme cela a et e d ej a mentionn e, l inconv enient principal de cette strat egie est qu elle exige un important espace m emoire. Ceci constitue un probl eme crucial pour des ex ecutions dans des ....

M. J. Quinn. Analysis and implementation of branch-and-bound algorithms on a hypercube multicomputer. IEEE Transaction on Computers, 39(3), March 1990.

....that contain a feasible solution and that, at any point of the execution, were generated but neither decomposed nor eliminated. At each iteration, the data structure D is composed of a collection of open subproblems, called 9 Or live nodes [30] active subproblems [57] unexamined nodes [52], frontier nodes [26] 4 openset 10 , an upper bound 11 U , which is the best value found so far, and a feasible solution whose value is U . The execution of the algorithm starts with the data structure in the initial state D 0 = fSg; U 0 ) where U 0 f is a constant corresponding ....

....smallest priority. A search tree T = V; fi) with the domain S, the objective function f and a lower bound function l, is called a BB tree [31] The leaves of T are solution nodes 14 , which solved directly in a decomposition. Let worthwhile subproblem 15 be a subproblem v so that l(v) f [52]. 10 Or liveset [31] active set [57] 11 Or incumbent [31] 12 Or bounding function [30] 13 Or least cost branch and bound [30] best bound first [31] best bound [24, 52, 53] The maximization version is also known as branching from the largest upper bound [16] 14 Or bottom nodes ....

[Article contains additional citation context not shown here]

M. Quinn. Analysis and Implementation of Branch and Bound Algorithms on a Hypercube Multicomputer. IEEE Trans. on Comp., 39(3):384--387, March 1990.

....to communication bottlenecks. Only if the computation time for one branching step is much larger than the communication time to transfer one load unit, bottlenecks can be avoided. The distributed implementation of branch bound was studied by several authors. Some of this work can be found in [1, 7, 9, 11, 12, 17, 18, 19, 24, 27, 31]. Distributed implementations of branch bound solving the traveling salesman problem can be found in [24, 4] Most of these work is done on smaller networks using branch and bound algorithms which are not as efficient as the ones described in [14] Therefore only relatively small instances of the ....

....load unit, bottlenecks can be avoided. The distributed implementation of branch bound was studied by several authors. Some of this work can be found in [1, 7, 9, 11, 12, 17, 18, 19, 24, 27, 31] Distributed implementations of branch bound solving the traveling salesman problem can be found in [24, 4]. Most of these work is done on smaller networks using branch and bound algorithms which are not as efficient as the ones described in [14] Therefore only relatively small instances of the traveling salesman problem could be solved using these algorithms . Our parallelization of this algorithm ....

M. J. Quinn, Analysis and Implementation of Branch and Bound Algorithms on a Hypercube Multicomputer, IEEE Transactions on Computers, Vol. 39, No. 3, 1990

....les strat egies d equilibrage de taches propos ees. La strat egie de choix du probl eme a traiter ou a envoyer, parmi les probl emes mis dans une file d attente, peu affecter consid erablement les performances du traitement parall ele. Notons dans ce contexte les travaux ayant et e faits par [Vor87, AM88, Fel88, LM89, Qui90, LM92, BC92], nous remarquons que Quinn [Qui90] Mans et Roucairol [BC92] ont bien montr e le bon impact d une strat egie meilleur d abord ( a meilleure evaluation) par rapport a une strat egie al eatoire (o u un probl eme est choisit al eatoirement) ou une strat egie profondeur d abord ....

....du probl eme a traiter ou a envoyer, parmi les probl emes mis dans une file d attente, peu affecter consid erablement les performances du traitement parall ele. Notons dans ce contexte les travaux ayant et e faits par [Vor87, AM88, Fel88, LM89, Qui90, LM92, BC92] nous remarquons que Quinn [Qui90], Mans et Roucairol [BC92] ont bien montr e le bon impact d une strat egie meilleur d abord ( a meilleure evaluation) par rapport a une strat egie al eatoire (o u un probl eme est choisit al eatoirement) ou une strat egie profondeur d abord (le choix du probl eme est fait par ....

[Article contains additional citation context not shown here]

M. J. Quinn. Analysis and implementation of branch-and-bound algorithms on a hypercube multicomputer. IEEE Transaction, 39(3), March 1990.

....correct. Results from this model have been verified on the parallel formulation of a DFS algorithm, called PODEM, which uses very powerful heuristics to order the search tree [7] 3.2 Parallel Best First Search. A number of researchers have investigated parallel formulations of A B B algorithms [35, 37, 43, 48, 64, 70, 77, 80]. An important component of A B B algorithms is the priority queue which is used to maintain the frontier (i:e: unexpanded) nodes of the search graph in a heuristic order. In the sequential A B B algorithm, in each cycle a most promising node from the priority queue is removed and expanded, ....

Michael J. Quinn. Analysis and implementation of branch-and-bound algorithms on a Hypercube multicomputer. IEEE Transactions on Computers, ?, 1989.

....computational work within the computer network. The importance of such a design aspect is to avoid the localization of the search of the branch and bound tree in terms of a single processor doing most of the useful work, as well as proceeding in a depth first fashion as opposed to a breadth first, [26]. The structure that is embedded within the topology of the computer network is also crucial in allowing faster diffusion through local information exchange, 27] This last point is very important since our target is to develop a distributed framework that is exclusively based on local ....

....the best lower bound. This heuristic aims at minimizing the probability 12 IOANNIS P. ANDROULAKIS, AND CHRISTODOULOS A. FLOUDAS of a single node performing most of the useful work by operating in a best first mode locally. Rare information exchanges are known to cause performance deterioration, [26], since if information exchange does not take place frequently, then the useful parts of the branch and bound tree are located in a single processor, and all useful work is limited. As can be seen from our computational results, shown in Figure 10, the work load distribution becomes more uneven as ....

M. Quinn, Analysis and implementation of branch and bound algorithms on a hypercube multicomputer, IEEE Transactions on Computers, 39 (1990), pp. 384-- 387.

....architectures. In particular, the scalability of this scheme is shown to be no worse than that of the best load balancing schemes on MIMD architectures. 4 Parallel Best First Search A number of researchers have investigated parallel formulations of A best first branch and bound (B B) algorithms [73, 79, 88, 107, 121, 47, 146, 151, 127, 40, 3, 18, 22, 67, 93, 134, 111, 112, 113, 116, 142, 102, 144, 101, 97]. An important component of A B B algorithms is the priority queue which is used to maintain the frontier (i:e: unexpanded) nodes of the search graph in a heuristic order. In the sequential A B B algorithm, in each cycle a most promising node from the priority queue is removed and expanded, ....

....expanded, and the newly generated nodes are added to the priority queue. In most parallel formulations of A , different processors concurrently expand different frontier nodes. Conceptually, these formulations differ in the data structures used to implement the priority queue of the A algorithm [104, 106, 107, 122, 121, 123, 46, 151]. Given P processors, the simplest parallel strategy is to let each parallel processor work on one of the P current best nodes in the OPEN list. This strategy is called the centralized strategy [104, 123, 46] because each processor gets work from the global OPEN list. As discussed in [52] this ....

Michael J. Quinn. Analysis and implementation of branch-and-bound algorithms on a Hypercube multicomputer. IEEE Transactions on Computers, 1989.

....to communication bottlenecks. Only if the computation time for one branching step is much larger than the communication time to transfer one load unit, bottlenecks can be avoided. The distributed implementation of branch bound was studied by several authors. Some of this work can be found in [1, 8, 10, 12, 17, 18, 19, 24, 27, 31, 32]. Distributed implementations of branch bound solving the traveling salesman problem can be found in [24, 5] Most of these work is done on smaller networks using branch and bound algorithms which are not as efficient as the ones described in [14] Therefore only relatively small instances of ....

....load unit, bottlenecks can be avoided. The distributed implementation of branch bound was studied by several authors. Some of this work can be found in [1, 8, 10, 12, 17, 18, 19, 24, 27, 31, 32] Distributed implementations of branch bound solving the traveling salesman problem can be found in [24, 5]. Most of these work is done on smaller networks using branch and bound algorithms which are not as efficient as the ones described in [14] Therefore only relatively small instances of the traveling salesman problem could be solved using these algorithms . Our parallelization of this algorithm is ....

M. J. Quinn, Analysis and Implementation of Branch and Bound Algorithms on a Hypercube Multicomputer, IEEE Transactions on Computers, Vol. 39, No. 3, 1990

....knowledge about the position of the solution in it. Nevertheless, the size of the search space still grows exponentially with the size of the input (see figure 1) Thus, it is until now an open research problem to study, and the main question which we try to answer with many other research teams [11, 8, 9, 1, 17, 10, 12, 18], is what can parallelism offer in solving NP complete combinatorial optimization problems. The B B algorithms use a large class of search techniques. Among them, there is the best first B B. This technique handles the subproblem with minimal bound. It leads to a very good computational ....

M.J. Quinn. Analysis and implementation of branchand -bound algorithms on a hypercube multiprocessor. IEEE Transacitons on Computers, 3(39):384--387, 1990.

....to a speedup of 29.38 on a network of 32 transputers. We did some experiments with this technique and found it not to be useful for larger networks, because of the poor balancing in the ending phase of the algorithm (only few subproblems in the network, but concentrated on some processors) Quinn [18] presents results for a round robin distribution of unexamined subproblems to the neighbors of a processor and studies the effects of different selection strategies for the subproblem that is sent during one migration phase. He compares simulation results that were computed on a 64 processor ....

M. J. Quinn, Analysis and Implementation of Branch and Bound Algorithms on a Hypercube Multicomputer, IEEE Transactions on Computers, Vol. 39, No. 3, 1990

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