**Speeding up dynamic programming**.

D. Eppstein, Z. Galil, and R. Giancarlo.

*29th IEEE Symp. Foundations of Comp. Sci.,*White Plains, New York, 1988, pp. 488–496.

*Worksh. Algorithms for Molecular Genetics,*Bethesda, Maryland, 1988.

Tech. Rep. CUCS-379-88, Computer Science Dept., Columbia University, 1988.

Appeared as "Efficient algorithms with applications to molecular biology" in*Int. Advanced Workshop on Sequences,*Positano, Italy, 1988.

*Sequences: Combinatorics, Compression, Security, Transmission,*R. M. Capocelli, ed., Springer, 1990, pp. 59–74.The FOCS and Positano versions of this paper merged my results on a dynamic program used for RNA secondary structure prediction, with Raffaele's on sequence comparison. The Bethesda talk and the TR version both used the longer title "Speeding up dynamic programming with application to the computation of RNA structure", and included only the RNA result, which used a mild convexity assumption on certain costs to save two orders of magnitude in total time. This work incited a boom in computational biology within the theory community that is still going strong. But the RNA results were quickly improved by a log factor [Aggarwal et al. at the same FOCS] and never made it into a journal paper.

(Bibtex: Positano, FOCS – Citations – Citations of "Efficient algorithms..." – MIT hypertext bibliography – CiteSeer)

**Sequence comparison with mixed convex and concave costs**.

D. Eppstein.

Tech. Rep. CUCS-382-88, Computer Science Dept., Columbia University, 1988.

*J. Algorithms*11 (1): 85–101, 1990.Gives an algorithm for finding the minimum number of mutations needed to transform one input string into another, in a general model in which substrings may be inserted or deleted at a cost depending nonlinearly on the substring length. The time bound depends on the number of times the second derivative of the cost function changes sign.

**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

*n*and^{2}*n*in the maximum length of reset sequences for general automata.^{3}(BibTeX – Citations – CiteSeer – ACM DL (ICALP) – ACM DL (SJC))

**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.

(BibTeX – Citations – CiteSeer – ACM DL (ARCS) – ACM DL (ICALP))

Years – Publications – David Eppstein – Theory Group – Inf. & Comp. Sci. – UC Irvine

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