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Load Balancing for Distributed Branch & Bound Algorithms
, 1992
"... In this paper, we present a new load balancing algorithm and its application to distributed branch & bound algorithms. We demonstrate the efficiency of this scheme by solving some NPcomplete problems on a network of up to 256 Transputers. The parallelization of our branch & bound algorithm is fully ..."
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Cited by 35 (7 self)
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In this paper, we present a new load balancing algorithm and its application to distributed branch & bound algorithms. We demonstrate the efficiency of this scheme by solving some NPcomplete problems on a network of up to 256 Transputers. The parallelization of our branch & bound algorithm is fully distributed. Every processor performs the same algorithm but on a different part of the solution tree. In this case, it is necessary to distribute subproblems among the processors to achieve a well balanced workload. We present a load balancing method which overcomes the problem of search overhead and idle times by an appropriate load model and avoids trashing effects by a feedback control strategy. To show the performance of our strategy, we solved the Vertex Cover and the weighted Vertex Cover problem for graphs of up to 150 nodes, using highly efficient branch and bound algorithms. Although the computing times were very short on a 256 processor network, we were able to achieve a speedup ...
A Distributed Processing Algorithm for Solving Integer Programs Using a Cluster of Workstations
 Parallel Computing
, 1994
"... The sequential Branch and Bound Algorithm is the most established method for solving Mixed Integer and Discrete Programming Problems. It is based on the tree search of the possible subproblems of the original problem. There are two goals in carrying out a tree search, namely, (i) finding a good and ..."
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Cited by 13 (0 self)
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The sequential Branch and Bound Algorithm is the most established method for solving Mixed Integer and Discrete Programming Problems. It is based on the tree search of the possible subproblems of the original problem. There are two goals in carrying out a tree search, namely, (i) finding a good and ultimately the best integer solution, and (ii) to prove that the best solution has been found or no integer feasible solution exists. We call these the stage 1 and stage 2 of tree search. In general it is extremely difficult to choose the ideal search strategy in stage 1 or stage 2 for a given integer programming (IP) problem. On the other hand by investigating a number of different strategies (and hence different search trees) a good solution can be reached quickly in respect of many practical IP problems. Starting from this observation a parallel branch and bound algorithm has been designed which exploits this two stage approach. In the first stage we investigate a number of alternative se...
Control Schemes in a Generalized Utility for Parallel BranchandBound Algorithms
 Proceedings of the 1997 Eleventh International Parallel Processing Symposium, IEEE Computer Society Press, Los Alamitos, CA
, 1997
"... Branchandbound algorithms are general methods applicable to various combinatorial optimization problems and parallelization is one of the most hopeful methods to improve these algorithms. Parallel branchandbound algorithm implementations can be divided in two types based on whether a central or ..."
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Cited by 11 (1 self)
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Branchandbound algorithms are general methods applicable to various combinatorial optimization problems and parallelization is one of the most hopeful methods to improve these algorithms. Parallel branchandbound algorithm implementations can be divided in two types based on whether a central or a distributed control scheme is used. Central control schemes have reduced scalability because of bottleneck problems frequently encountered. In order to solve problem cases that cannot be solved with sequential branchandbound algorithm, distributed control schemes are necessary. However, compared to central control schemes, higher efficiency is not always achieved through the use of a distributed control scheme. In this paper, a mixed control scheme is proposed, changing between the two different types of control schemes during execution. In addition, a dynamic load balancing strategy is applied in the distributed control scheme. Performance evaluation for three different cases is carried...
Distributed Combinatorial Optimization
 PROC. OF SOFSEM'93, CZECH REPUBLIK
, 1993
"... This paper reports about research projects of the University of Paderborn in the field of distributed combinatorial optimization. We give an introduction into combinatorial optimization and a brief definition of some important applications. As a first exact solution method we describe branch & boun ..."
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Cited by 10 (6 self)
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This paper reports about research projects of the University of Paderborn in the field of distributed combinatorial optimization. We give an introduction into combinatorial optimization and a brief definition of some important applications. As a first exact solution method we describe branch & bound and present the results of our work on its distributed implementation. Results of our distributed implementation of iterative deepening conclude the first part about exact methods. In the second part we give an introduction into simulated annealing as a heuristic method and present results of its parallel implementation. This part is concluded with a brief description of genetic algorithms and some other heuristic methods together with some results of their distributed implementation.
Solving the Traveling Salesman Problem with a Distributed BranchandBound Algorithm on a 1024 Processor Network
, 1995
"... This paper is the first to present a parallelization of a highly efficient bestfirst branchandbound algorithm to solve large symmetric traveling salesman problems on a massively parallel computer containing 1024 processors. The underlying sequential branchandbound algorithm is based on 1tree r ..."
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Cited by 7 (2 self)
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This paper is the first to present a parallelization of a highly efficient bestfirst branchandbound algorithm to solve large symmetric traveling salesman problems on a massively parallel computer containing 1024 processors. The underlying sequential branchandbound algorithm is based on 1tree relaxation. The parallelization of the branchandbound algorithm is fully distributed. Every processor performs the same sequential algorithm but on a different part of the solution tree. To distribute subproblems among the processors we use a new directneighbor dynamic loadbalancing strategy. The general principle can be applied to all other branchandbound algorithms leading to an "automatic" parallelization. At present we can efficiently solve traveling salesman problems up to a size of 318 cities on networks of up to 1024 transputers. On hard problems we achieve an almost linear speedup. 1 Introduction The efficient solution of large combinatorial optimization problems is highly imp...
Dynamic Load Balancing for Parallel IntervalNewton Using Message Passing
, 2002
"... Branchandprune (BP) and branchandbound (BB) techniques are commonly used for intelligent search in finding all solutions, or the optimal solution, within a space of interest. The corresponding binary tree structure provides a natural parallelism allowing concurrent evaluation of subproblems usin ..."
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Cited by 5 (3 self)
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Branchandprune (BP) and branchandbound (BB) techniques are commonly used for intelligent search in finding all solutions, or the optimal solution, within a space of interest. The corresponding binary tree structure provides a natural parallelism allowing concurrent evaluation of subproblems using parallel computing technology. Of special interest here are techniques derived from interval analysis, in particular an intervalNewton/generalizedbisection procedure. In this context, we discuss issues of load balancing and work scheduling that arise in the implementation of parallel intervalNewton on a cluster of workstations using message passing, and describe and analyze techniques for this purpose. Results using an asynchronous diffusive load balancing strategy show that a consistently high efficiency can be achieved in solving nonlinear equations, providing excellent scalability, especially with the use of a twodimensional torus virtual network. The effectiveness of the approach used, especially in connection with a novel stack management scheme, is also demonstrated in the consistent superlinear speedups observed in performing global optimization.
Solving the traveling salesman problem with a parallel branchandbound algorithm on a 1024 processor network
 DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE
, 1994
"... This paper is the first to present a parallelization of a higly efficient bestfirst branchandbound algorithm to solve large symmetric traveling saleman problems on a massively parallel computer containing 1024 processors. The underlying sequential branch &bound algorithm is based on 1tree relaxa ..."
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Cited by 4 (0 self)
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This paper is the first to present a parallelization of a higly efficient bestfirst branchandbound algorithm to solve large symmetric traveling saleman problems on a massively parallel computer containing 1024 processors. The underlying sequential branch &bound algorithm is based on 1tree relaxation introduced by Held and Karp (Lagrangean approach) and improved by Volgenant and Jonker. The parallelization of the branch & bound algorithm is fully distributed. Every processor performs the same sequential algorithm but on a different part of the solution tree. To distribute subproblems among the processors we use a new directneighbor dynamic loadbalancing strategy. The general principle can be applied to all other branchandbound algorithms leading to an "automatic " parallelization. At present we can efficiently solve traveling salesman problems up to a size of 318 cities on networks of up to 1024 transputers. On hard problems we achieve an almost linear speedup.
Compressing CubeConnected Cycles and Butterfly Networks
 Proc. 2nd IEEE Symposium on Parallel and Distributed Processing
, 1990
"... We consider the simulation of large cubeconnected cycles (CCC) and large butterfly networks (BFN) on smaller ones, a problem that arises when algorithms designed for an architecture of an ideal size are to be executed on an existing architecture of a fixed size. We show that large CCC's and BFN 's ..."
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Cited by 4 (4 self)
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We consider the simulation of large cubeconnected cycles (CCC) and large butterfly networks (BFN) on smaller ones, a problem that arises when algorithms designed for an architecture of an ideal size are to be executed on an existing architecture of a fixed size. We show that large CCC's and BFN 's can be embedded into smaller networks of the same type with (a) dilation 2 and optimum load, (b) dilation 1 and optimum load in most cases, (c) dilation 1 and nearly optimum load in all cases. Our results show that large CCC's and BFN 's can be simulated very efficiently on smaller ones. Additionally, we implemented our algorithm for compressing CCC's and ran several experiments on a Transputer network, which showed that our technique also behaves very well from a practical point of view. A preliminary version of these results appears in: Proc. 2nd IEEE Symposium on Parallel and Distributed Processing (1990), pp. 858865. y This work was supported by grant Mo 285/41 from the German Re...
Solving largescale traveling salesman problems with parallel BranchandCut
, 1995
"... We introduce the implementation of a parallel BranchandCut algorithm to solve largescale traveling salesman problems. Rather than using the wellknown models of homogeneous distribution and simple Master/Slave communication, we present a more sophisticated distribution that takes the advantage of ..."
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Cited by 2 (0 self)
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We introduce the implementation of a parallel BranchandCut algorithm to solve largescale traveling salesman problems. Rather than using the wellknown models of homogeneous distribution and simple Master/Slave communication, we present a more sophisticated distribution that takes the advantage of several independent features of a BranchandCut code. Computational results are reported for several instances of the TSPLIB.
LogP Analysis of Parallel Branch and Bound for Graph Coloring
 IEEE Transactions on Parallel and Distributed Systems
, 1994
"... We examine implementations of a parallel branch and bound algorithm for coloring graphs on the Connection Machine CM5. Using the LogP model of parallel computation, an asynchronous model aiming to capture the communication costs of a family of architectures including the CM5, we examine three load ..."
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Cited by 1 (0 self)
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We examine implementations of a parallel branch and bound algorithm for coloring graphs on the Connection Machine CM5. Using the LogP model of parallel computation, an asynchronous model aiming to capture the communication costs of a family of architectures including the CM5, we examine three load balancing strategies: busy processors sending work randomly to other processors (Random); idle processors polling other processors for work (Polling); and matching busy processors with idle processors using a manager (MatchMaker) . This is the first use of LogP for analyzing problems with unstructured communication patterns. The analysis divides the computation into three phases: startup phases during which one or a few processors have work and need to distribute it quickly to all the other processors; busy phases during which there is plenty of work for all processors; and sparse phases during which the amount of work is limited. The analysis uses LogP to find ratios of time spent on comm...