Showing papers by "Robert E. Tarjan published in 1997"

Faster and simpler algorithm for sorting signed permutations by reversals

Abstract: We give a quadratic algorithm for finding the minimum number of reversals needed to sort a signed permutation. Our algorithm is faster than the previous algorithm of Hannenhalli and Pevzner and its faster implementation of Berman and Hannenhalli. The algorithm is conceptually simple and does not require special data structures. Our study also considerably simplifies the combinatorial structures used by the analysis. 2 refs.

Dynamic trees as search trees via Euler tours, applied to the network simplex algorithm

Abstract: Thedynamic tree is an abstract data type that allows the maintenance of a collection of trees subject to joining by adding edges (linking) and splitting by deleting edges (cutting), while at the same time allowing reporting of certain combinations of vertex or edge values. For many applications of dynamic trees, values must be combined along paths. For other applications, values must be combined over entire trees. For the latter situation, an idea used originally in parallel graph algorithms, to represent trees by Euler tours, leads to a simple implementation with a time of O(logn) per tree operation, wheren is the number of tree vertices. We apply this representation to the implementation of two versions of the network simplex algorithm, resulting in a time of O(logn) per pivot, wheren is the number of vertices in the problem network.

Faster and simpler algorithm for sorting signed permutations by reversals

Abstract: We give a quadratic algorithm for finding the minimum number of reversals needed to sort a signed permutation. Our algorithm is faster than the previous algorithm of Hannenhalli and Pevzner and its faster implementation of Berman and Hannenhalli. The algorithm is conceptually simple and does not require special data structures. Our study also considerably simplifies the combinatorial structures used by the analysis. 2 refs.

Optimal parallel verification of minimum spanning trees in logarithmic time

Abstract: We present the first optimal parallel algorithms for the verification and sensitivity analysis of minimum spanning trees. Our algorithms are deterministic and run inO(logn) time and require linear-work in the CREW PRAM model. These algorithms are used as a subroutine in the linear-work randomized algorithm for finding minimum spanning trees of Cole, Klein, and Tarjan.

Toward Efficient Unstructured Multigrid Preprocessing

Abstract: The multigrid method is a general and powerful means of accelerating the convergence of discrete iterative methods for solving partial differential equations PDEs and similar problems. The adaptation of the multigrid method to un structured meshes is important in solving problems with complex geometries. Such problems lie on the forefront of many scientific and engineering fields. Unfortunately, multi grid schemes on unstructured meshes require signifi cantly more preprocessing than on structured meshes. In fact, preprocessing can be a major part of the solution task and, for many applications, must be executed repeatedly. In addition, the large computational requirements of real istic PDEs, accurately discretized on unstructured meshes, make such computations candidates for parallel or distributed processing. This adds problem partitioning as a preprocessing task. We propose and examine experi mentally an automatic and unified strategy to perform several unstructured multigrid preprocessing tasks. Our strategy is based on dominating sets in the unstructured meshes. We also suggest several alternative related strategies. Our experiments evaluate the performance of two preprocessing tasks: coarse-mesh generation and domain partitioning. The experiments suggest that our preprocessing strategy produces high-quality meshes that give good multigrid performance. Our strategy also pro duces domain partitions that are reasonably load bal anced with relatively small edge cuts. Overall, we conclude that simple, integrated algorithmic strategies and data structures can make tedious preprocessing tasks more efficient and more automated-a necessary step toward the practical application of unstructured multigrid methods.