Parallel algorithms
Reset sequences for monotonic automata.
D. Eppstein.
15th Int. Coll. Automata, Languages and Programming, Tampere, Finland, 1988.
Springer, Lecture Notes in Comp. Sci. 317, 1988, pp. 230–238.
SIAM J. Computing 19 (3): 500–510, 1990.Automata theory. A reset sequence for a DFA is an input such that, no matter which state the DFA starts in, it ends up after the input in a known state. These have been used by Natarajan and Goldberg for certain robot motion planning problems (in fact the conference version of this paper used the title "Reset sequences for finite automata with application to design of parts orienters"), and also in coding theory where they arise in the design of self-synchronizing codes. This paper considers DFAs in which the transition functions respect a given cyclic ordering of the states, and shows that their shortest reset sequences can be found quickly. It also considers parallel algorithms for the problem. There remains open a gap between n2 and n3 in the maximum length of reset sequences for general automata.
Parallel algorithmic techniques for combinatorial computation.
D. Eppstein and Z. Galil.
Ann. Rev. Comput. Sci. 3: 233–283, 1988.
Invited talk by Z. Galil, 16th Int. Coll. Automata, Languages and Programming, Stresa, Italy, 1989.
Springer, Lecture Notes in Comp. Sci. 372, 1989, pp. 304–318.This survey on parallel algorithms emphasized the use of basic subroutines such as prefix sums, Euler tours, ear decomposition, and matrix multiplication for solving more complicated graph problems.
Planar orientations with low out-degree and compaction of adjacency matrices.
M. Chrobak and D. Eppstein.
Theor. Comp. Sci. 86 (2): 243–266, 1991.Describes efficient sequential and parallel algorithms for orienting the edges of an undirected planar graph so that each vertex has few outgoing edges. From such an orientation one can test in constant time whether a given edge exists. More recently this paper has been cited for its applications to scheduling update operations in parallel finite element methods.
Fast optimal parallel algorithms for maximal matching in sparse graphs.
H. Asuri, M. Dillencourt, D. Eppstein, G. Lueker, and M. Molodowitch.
Tech. Rep. 92-01, ICS, UCI, 1992.We later discovered that the same results were published in a SPAA paper by Greg Shannon.
Parallel recognition of series parallel graphs.
D. Eppstein.
Information & Computation 98: 41–55, 1992.Characterizes two-terminal series graphs in terms of a tree-like structure in their ear decompositions. Uses this characterization to construct parallel algorithms that recognize these graphs and construct their series-parallel decompositions.
Efficient sequential and parallel algorithms for computing recovery points in trees and paths.
M. Chrobak, D. Eppstein, G.F. Italiano, and M. Yung.
2nd ACM-SIAM Symp. Discrete Algorithms, San Francisco, 1991, pp. 158–167.
ALCOM Report 91-74, University of Rome, 1991.Described slightly superlinear algorithms for partitioning a tree into a given number of subtrees, making them all as short as possible. Frederickson at the same conference further improved the sequential time to linear. There may still be something worth publishing in the parallel algorithms.
Parallel construction of quadtrees and quality triangulations.
M. Bern, D. Eppstein, and S.-H. Teng.
3rd Worksh. Algorithms and Data Structures, Montreal, 1993.
Springer, Lecture Notes in Comp. Sci. 709, 1993, pp. 188–199.
Tech. Rep. 614, MIT Lab. for Comp. Sci., 1994.
Int. J. Comp. Geom. & Appl. 9 (6): 517–532, 1999.A parallelization of the quadtree constructions in "Provably good mesh generation", in an integer model of computation, based on a technique of sorting the input points using values formed by shuffling the binary representations of the coordinates. A side-effect is an efficient construction for the "fair split tree" hierarchical clustering method used by Callahan and Kosaraju for various nearest neighbor problems.