We survey recent trends in practical algorithms for balanced graph partitioning, point to applications and discuss future research directions.

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Recent Advances in Graph Partitioning

We present a detailed and up-to-date survey of the literature on parallel branch-and-bound algorithms. We synthesize previous work in this area and propose a new classification of parallel branch-and-bound algorithms. This classification is used to analyze the methods proposed in the literature. To facilitate our analysis, we give a new characterization of branch-and-bound algorithms, which consists of isolating the performed operations without specifying any particular order for their execution.

Parallel Branch-and-Branch Algorithms: Survey and Synthesis

DIB is a general-purpose package that allows a wide range of applications such as recursive backtrack, branch and bound, and alpha-beta search to be implemented on a multicomputer. It is very easy to use. The application program needs to specify only the root of the recursion tree, the computation to be performed at each node, and how to generate children at each node. In addition, the application program may optionally specify how to synthesize values of tree nodes from their children's values and how to disseminate information (such as bounds) either globally or locally in the tree. DIB uses a distributed algorithm, transparent to the application programmer, that divides the problem into subproblems and dynamically allocates them to any number of (potentially nonhomogeneous) machines. This algorithm requires only minimal support from the distributed operating system. DIB can recover from failures of machines even if they are not detected. DIB currently runs on the Crystal multicomputer at the University of Wisconsin-Madison. Many applications have been implemented quite easily, including exhaustive traversal (N queens, knight's tour, negamax tree evaluation), branch and bound (traveling salesman) and alpha-beta search (the game of NIM). Speedup is excellent for exhaustive traversal and quite good for branch and bound.

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DIB—a distributed implementation of backtracking

In this paper, the authors present a detailed and up-to-date survey of the literature on parallel branch-and-bound algorithms. They synthesize previous work in this area and propose a new classification of parallel branch-and-bound algorithms. This classification is used to analyze the methods proposed in the literature. To facilitate their analysis, they give a new characterization of branch-and-bound algorithms, which consists of isolating the performed operations withous specifying any particular order for their execution. (A)

Parallel branch-and-bound algorithms: survey and synthesis

In recent years, Massively Parallel Processors (MPPs) have gained ground enabling vast amounts of data processing. In such environments, data is partitioned across multiple compute nodes, which results in dramatic performance improvements during parallel query execution. To evaluate certain relational operators in a query correctly, data sometimes needs to be re-partitioned (i.e., moved) across compute nodes. Since data movement operations are much more expensive than relational operations, it is crucial to design a suitable data partitioning strategy that minimizes the cost of such expensive data transfers. A good partitioning strategy strongly depends on how the parallel system would be used. In this paper we present a partitioning advisor that recommends the best partitioning design for an expected workload. Our tool recommends which tables should be replicated (i.e., copied into every compute node) and which ones should be distributed according to specific column(s) so that the cost of evaluating similar workloads is minimized. In contrast to previous work, our techniques are deeply integrated with the underlying parallel query optimizer, which results in more accurate recommendations in a shorter amount of time. Our experimental evaluation using a real MPP system, Microsoft SQL Server 2008 Parallel Data Warehouse, with both real and synthetic workloads shows the effectiveness of the proposed techniques and the importance of deep integration of the partitioning advisor with the underlying query optimizer.

Automated partitioning design in parallel database systems

Consideration is given to the performance of parallel best-bound-first branch-and-bound algorithms in which several nodes with least lower bounds are expanded simultaneously. It is well known that anomalies may occur in the execution of a parallel branch-and-bound algorithm. The authors show the conditions under which anomalies are guaranteed not to occur when the number of processors is doubled, or not even doubled.

Ten-Hwang Lai

Papers

Performance of parallel branch-and-bound algorithms

The complexity of congestion-1 embedding in a hypercube

Bipartite permutation graphs with application to the minimum buffer size problem

On the routability of a convex grid

Algorithms for page retrieval and Hamiltonian paths on forward-convex line graphs