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15
Estimating Search Tree Size
 In Proceedings of the 21st National Conference on Artificial Intelligence (AAAI ’06
, 2006
"... We propose two new online methods for estimating the size of a backtracking search tree. The first method is based on a weighted sample of the branches visited by chronological backtracking. The second is a recursive method based on assuming that the unexplored part of the search tree will be simil ..."
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Cited by 26 (2 self)
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We propose two new online methods for estimating the size of a backtracking search tree. The first method is based on a weighted sample of the branches visited by chronological backtracking. The second is a recursive method based on assuming that the unexplored part of the search tree will be similar to the part we have so far explored. We compare these methods against an old method due to Knuth based on random probing. We show that these methods can reliably estimate the size of search trees explored by both optimization and decision procedures. We also demonstrate that these methods for estimating search tree size can be used to select the algorithm likely to perform best on a particular problem instance.
Embarrassingly parallel search
 Principles and Practice of Constraint Programming
, 2013
"... Abstract. We propose the Embarrassingly Parallel Search, a simple and efficient method for solving constraint programming problems in parallel. We split the initial problem into a huge number of independent subproblems and solve them with available workers, for instance cores of machines. The decomp ..."
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Abstract. We propose the Embarrassingly Parallel Search, a simple and efficient method for solving constraint programming problems in parallel. We split the initial problem into a huge number of independent subproblems and solve them with available workers, for instance cores of machines. The decomposition into subproblems is computed by selecting a subset of variables and by enumerating the combinations of values of these variables that are not detected inconsistent by the propagation mechanism of a CP Solver. The experiments on satisfaction problems and optimization problems suggest that generating between thirty and one hundred subproblems per worker leads to a good scalability. We show that our method is quite competitive with the work stealing approach and able to solve some classical problems at the maximum capacity of the multicore machines. Thanks to it, a user can parallelize the resolution of its problem without modifying the solver or writing any parallel source code and can easily replay the resolution of a problem. 1
Basis reduction and the complexity of branchandbound
"... The classical branchandbound algorithm for the integer feasibility problem ..."
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Cited by 7 (0 self)
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The classical branchandbound algorithm for the integer feasibility problem
Could we use a million cores to solve an integer program?
 Mathematical Methods of Operations Research
, 2012
"... Abstract Given the steady increase in cores per CPU, it is only a matter of time before supercomputers will have a million or more cores. In this article, we investigate the opportunities and challenges that will arise when trying to utilize this vast computing power to solve a single integer linea ..."
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Abstract Given the steady increase in cores per CPU, it is only a matter of time before supercomputers will have a million or more cores. In this article, we investigate the opportunities and challenges that will arise when trying to utilize this vast computing power to solve a single integer linear optimization problem. We also raise the question of whether best practices in sequential solution of ILPs will be effective in massively parallel environments.
Solving Hard Mixed Integer Programming Problems with XpressMP: A MIPLIB 2003 Case Study
, 2007
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A Case Study in Complexity Estimation: Towards Parallel BranchandBound over Graphical Models
"... We study the problem of complexity estimation in the context of parallelizing an advanced Branch and Boundtype algorithm over graphical models. The algorithm’s pruning power makes load balancing, one crucial element of every distributed system, very challenging. We propose using a statistical regre ..."
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We study the problem of complexity estimation in the context of parallelizing an advanced Branch and Boundtype algorithm over graphical models. The algorithm’s pruning power makes load balancing, one crucial element of every distributed system, very challenging. We propose using a statistical regression model to identify and tackle disproportionally complex parallel subproblems, the cause of load imbalance, ahead of time. The proposed model is evaluated and analyzed on various levels and shown to yield robust predictions. We then demonstrate its effectiveness for load balancing in practice. 1
Exploiting erraticism in search
 SUBMITTED TO OPERATIONS RESEARCH
, 2012
"... Highsensitivity to initial conditions is generally viewed as a drawback of tree search methods, as it leads to an erratic behavior to be mitigated somehow. In this paper we investigate the opposite viewpoint, and consider this behavior as an opportunity to exploit. Our working hypothesis is that er ..."
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Cited by 3 (3 self)
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Highsensitivity to initial conditions is generally viewed as a drawback of tree search methods, as it leads to an erratic behavior to be mitigated somehow. In this paper we investigate the opposite viewpoint, and consider this behavior as an opportunity to exploit. Our working hypothesis is that erraticism is in fact just a consequence of the exponential nature of tree search, that acts as a chaotic amplifier, so it is largely unavoidable. We propose a betandrun approach to actually turn erraticism to one’s advantage. The idea is to make a number of short sample runs with randomized initial conditions, to bet on the “most promising” run selected according to certain simple criteria, and to bring it to completion. Computational results on a large testbed of mixedinteger linear programs from the literature are presented, showing the potential of this approach even when embedded in a proofofconcept implementation.
Load Balancing for Parallel Branch and Bound
 In Proceedings of 10th Workshop on Preferences and Soft Constraints
, 2010
"... Abstract. A strategy for parallelization of a stateoftheart Branch and Bound algorithm for weighted CSPs and other graphical model optimization tasks is introduced: independent worker nodes concurrently solve subproblems, managed by a Branch and Bound master node; the problem cost functions are u ..."
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Abstract. A strategy for parallelization of a stateoftheart Branch and Bound algorithm for weighted CSPs and other graphical model optimization tasks is introduced: independent worker nodes concurrently solve subproblems, managed by a Branch and Bound master node; the problem cost functions are used to predict subproblem complexity, enabling efficient load balancing, which is crucial for the performance of the parallelization process. Experimental evaluation on up to 20 nodes yields very promising results and suggests the effectiveness of the scheme. The system runs on loosely coupled commodity hardware, simplifying deployment on a larger scale in the future. 1
FINDING MOST LIKELY HAPLOTYPES IN GENERAL PEDIGREES THROUGH PARALLEL SEARCH WITH DYNAMIC LOAD BALANCING
"... General pedigrees can be encoded as Bayesian networks, where the common MPE query corresponds to finding the most likely haplotype configuration. Based on this, a strategy for grid parallelization of a stateoftheart Branch and Bound algorithm for MPE is introduced: independent worker nodes concurr ..."
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General pedigrees can be encoded as Bayesian networks, where the common MPE query corresponds to finding the most likely haplotype configuration. Based on this, a strategy for grid parallelization of a stateoftheart Branch and Bound algorithm for MPE is introduced: independent worker nodes concurrently solve subproblems, managed by a Branch and Bound master node. The likelihood functions are used to predict subproblem complexity, enabling efficient automation of the parallelization process. Experimental evaluation on up to 20 parallel nodes yields very promising results and suggest the effectiveness of the scheme, solving several very hard problem instances. The system runs on loosely coupled commodity hardware, simplifying deployment on a larger scale in the future. 1.
Learning subproblem complexities in distributed branch and bound
 In Discrete Optimization for Learning Workshop NIPS
, 2011
"... In the context of distributed Branch and Bound Search for Graphical Models, effective load balancing is crucial yet hard to achieve due to early pruning of search branches. This paper proposes learning a regression model over structural as well as cost functionbased features to more accurately pred ..."
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In the context of distributed Branch and Bound Search for Graphical Models, effective load balancing is crucial yet hard to achieve due to early pruning of search branches. This paper proposes learning a regression model over structural as well as cost functionbased features to more accurately predict subproblem complexity ahead of time, thereby enabling more balanced parallel workloads. Early results show the promise of this approach. 1